prime.c

/*
 * prime - quickly determine if a small number is prime
 *
 * Copyright (C) 1999-2007,2021  Landon Curt Noll
 *
 * Calc is open software; you can redistribute it and/or modify it under
 * the terms of the version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * Calc is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 * Public License for more details.
 *
 * A copy of version 2.1 of the GNU Lesser General Public License is
 * distributed with calc under the filename COPYING-LGPL.  You should have
 * received a copy with calc; if not, write to Free Software Foundation, Inc.
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * Under source code control:   1994/06/04 03:26:14
 * File existed as early as:    1994
 *
 * chongo <was here> /\oo/\     http://www.isthe.com/chongo/
 * Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
 */


#include "qmath.h"
#include "prime.h"
#include "jump.h"
#include "have_const.h"


#include "banned.h"     /* include after system header <> includes */


/*
 * odd prime bitmap for odd values < 2^16
 *
 * pr_map[i] & (1<<j) == 1  ==>  i*16 + j*2 + 1 is prime
 *                       0  ==>  i*16 + j*2 + 1 is not prime
 *
 * This table is useful to quickly determine if a 16 bit odd number
 * is prime.  Use the prime[] array to quickly walk thru the 16 bit
 * off primes.
 */
CONST unsigned char pr_map[(MAX_MAP_VAL/8)+1] = {
    110,203,180,100,154, 18,109,129, 50, 76, 74,134, 13,130,150, 33,
    201, 52,  4, 90, 32, 97,137,164, 68, 17,134, 41,209,130, 40, 74,
     48, 64, 66, 50, 33,153, 52,  8, 75,  6, 37, 66,132, 72,138, 20,
      5, 66, 48,108,  8,180, 64, 11,160,  8, 81, 18, 40,137,  4,101,
    152, 48, 76,128,150, 68, 18,128, 33, 66, 18, 65,201,  4, 33,192,
     50, 45,152,  0,  0, 73,  4,  8,129,150,104,130,176, 37,  8, 34,
     72,137,162, 64, 89, 38,  4,144,  6, 64, 67, 48, 68,146,  0,105,
     16,130,  8,  8,164, 13, 65, 18, 96,192,  0, 36,210, 34, 97,  8,
    132,  4, 27,130,  1,211, 16,  1,  2,160, 68,192, 34, 96,145, 20,
     12, 64,166,  4,210,148, 32,  9,148, 32, 82,  0,  8, 16,162, 76,
      0,130,  1, 81, 16,  8,139,164, 37,154, 48, 68,129, 16, 76,  3,
      2, 37, 82,128,  8, 73,132, 32, 80, 50,  0, 24,162, 64, 17, 36,
     40,  1,132,  1,  1,160, 65, 10, 18, 69,  0, 54,  8,  0, 38, 41,
    131,130, 97,192,128,  4, 16, 16,109,  0, 34, 72, 88, 38, 12,194,
     16, 72,137, 36, 32, 88, 32, 69,136, 36,  0, 25,  2, 37,192, 16,
    104,  8, 20,  1,202, 50, 40,128,  0,  4, 75, 38,  0, 19,144, 96,
    130,128, 37,208,  0,  1, 16, 50, 12, 67,134, 33, 17,  0,  8, 67,
     36,  4, 72, 16, 12,144,146,  0, 67, 32, 45,  0,  6,  9,136, 36,
     64,192, 50,  9,  9,130,  0, 83,128,  8,128,150, 65,129,  0, 64,
     72, 16, 72,  8,150, 72, 88, 32, 41,195,128, 32,  2,148, 96,146,
      0, 32,129, 34, 68, 16,160,  5, 64,144,  1, 73, 32,  4, 10,  0,
     36,137, 52, 72, 19,128, 44,192,130, 41,  0, 36, 69,  8,  0,  8,
    152, 54,  4, 82,132,  4,208,  4,  0,138,144, 68,130, 50,101, 24,
    144,  0, 10,  2,  1, 64,  2, 40, 64,164,  4,146, 48,  4, 17,134,
      8, 66,  0, 44, 82,  4,  8,201,132, 96, 72, 18,  9,153, 36, 68,
      0, 36,  0,  3, 20, 33,  0, 16,  1, 26, 50,  5,136, 32, 64, 64,
      6,  9,195,132, 64,  1, 48, 96, 24,  2,104, 17,144, 12,  2,162,
      4,  0,134, 41,137, 20, 36,130,  2, 65,  8,128,  4, 25,128,  8,
     16, 18,104, 66,164,  4,  0,  2, 97, 16,  6, 12, 16,  0,  1, 18,
     16, 32,  3,148, 33, 66, 18,101, 24,148, 12, 10,  4, 40,  1, 20,
     41, 10,164, 64,208,  0, 64,  1,144,  4, 65, 32, 45, 64,130, 72,
    193, 32,  0, 16, 48,  1,  8, 36,  4, 89,132, 36,  0,  2, 41,130,
      0, 97, 88,  2, 72,129, 22, 72, 16,  0, 33, 17,  6,  0,202,160,
     64,  2,  0,  4,145,176,  0, 66,  4, 12,129,  6,  9, 72, 20, 37,
    146, 32, 37, 17,160,  0, 10,134, 12,193,  2, 72,  0, 32, 69,  8,
     50,  0,152,  6,  4, 19, 34,  0,130,  4, 72,129, 20, 68,130, 18,
     36, 24, 16, 64, 67,128, 40,208,  4, 32,129, 36,100,216,  0, 44,
      9, 18,  8, 65,162,  0,  0,  2, 65,202, 32, 65,192, 16,  1, 24,
    164,  4, 24,164, 32, 18,148, 32,131,160, 64,  2, 50, 68,128,  4,
      0, 24,  0, 12, 64,134, 96,138,  0,100,136, 18,  5,  1,130,  0,
     74,162,  1,193, 16, 97,  9,  4,  1,136,  0, 96,  1,180, 64,  8,
      6,  1,  3,128,  8, 64,148,  4,138, 32, 41,128,  2, 12, 82,  2,
      1, 66,132,  0,128,132,100,  2, 50, 72,  0, 48, 68, 64, 34, 33,
      0,  2,  8,195,160,  4,208, 32, 64, 24, 22, 64, 64,  0, 40, 82,
    144,  8,130, 20,  1, 24, 16,  8,  9,130, 64, 10,160, 32,147,128,
      8,192,  0, 32, 82,  0,  5,  1, 16, 64, 17,  6, 12,130,  0,  0,
     75,144, 68,154,  0, 40,128,144,  4, 74,  6,  9, 67,  2, 40,  0,
     52,  1, 24,  0,101,  9,128, 68,  3,  0, 36,  2,130, 97, 72, 20,
     65,  0, 18, 40,  0, 52,  8, 81,  4,  5, 18,144, 40,137,132, 96,
     18, 16, 73, 16, 38, 64, 73,130,  0,145, 16,  1, 10, 36, 64,136,
     16, 76, 16,  4,  0, 80,162, 44, 64,144, 72, 10,176,  1, 80, 18,
      8,  0,164,  4,  9,160, 40,146,  2,  0, 67, 16, 33,  2, 32, 65,
    129, 50,  0,  8,  4, 12, 82,  0, 33, 73,132, 32, 16,  2,  1,129,
     16, 72, 64, 34,  1,  1,132,105,193, 48,  1,200,  2, 68,136,  0,
     12,  1,  2, 45,192, 18, 97,  0,160,  0,192, 48, 64,  1, 18,  8,
     11, 32,  0,128,148, 64,  1,132, 64,  0, 50,  0, 16,132,  0, 11,
     36,  0,  1,  6, 41,138,132, 65,128, 16,  8,  8,148, 76,  3,128,
      1, 64,150, 64, 65, 32, 32, 80, 34, 37,137,162, 64, 64,164, 32,
      2,134, 40,  1, 32, 33, 74, 16,  8,  0, 20,  8, 64,  4, 37, 66,
      2, 33, 67, 16,  4,146,  0, 33, 17,160, 76, 24, 34,  9,  3,132,
     65,137, 16,  4,130, 34, 36,  1, 20,  8,  8,132,  8,193,  0,  9,
     66,176, 65,138,  2,  0,128, 54,  4, 73,160, 36,145,  0,  0,  2,
    148, 65,146,  2,  1,  8,  6,  8,  9,  0,  1,208, 22, 40,137,128,
     96,  0,  0,104,  1,144, 12, 80, 32,  1, 64,128, 64, 66, 48, 65,
      0, 32, 37,129,  6, 64, 73,  0,  8,  1, 18, 73,  0,160, 32, 24,
     48,  5,  1,166,  0, 16, 36, 40,  0,  2, 32,200, 32,  0,136, 18,
     12,144,146,  0,  2, 38,  1, 66, 22, 73,  0,  4, 36, 66,  2,  1,
    136,128, 12, 26,128,  8, 16,  0, 96,  2,148, 68,136,  0,105, 17,
     48,  8, 18,160, 36, 19,132,  0,130,  0,101,192, 16, 40,  0, 48,
      4,  3, 32,  1, 17,  6,  1,200,128,  0,194, 32,  8, 16,130, 12,
     19,  2, 12, 82,  6, 64,  0,176, 97, 64, 16,  1,152,134,  4, 16,
    132,  8,146, 20, 96, 65,128, 65, 26, 16,  4,129, 34, 64, 65, 32,
     41, 82,  0, 65,  8, 52, 96, 16,  0, 40,  1, 16, 64,  0,132,  8,
     66,144, 32, 72,  4,  4, 82,  2,  0,  8, 32,  4,  0,130, 13,  0,
    130, 64,  2, 16,  5, 72, 32, 64,153,  0,  0,  1,  6, 36,192,  0,
    104,130,  4, 33, 18, 16, 68,  8,  4,  0, 64,166, 32,208, 22,  9,
    201, 36, 65,  2, 32, 12,  9,146, 64, 18,  0,  0, 64,  0,  9, 67,
    132, 32,152,  2,  1, 17, 36,  0, 67, 36,  0,  3,144,  8, 65, 48,
     36, 88, 32, 76,128,130,  8, 16, 36, 37,129,  6, 65,  9, 16, 32,
     24, 16, 68,128, 16,  0, 74, 36, 13,  1,148, 40,128, 48,  0,192,
      2, 96, 16,132, 12,  2,  0,  9,  2,130,  1,  8, 16,  4,194, 32,
    104,  9,  6,  4, 24,  0,  0, 17,144,  8, 11, 16, 33,130,  2, 12,
     16,182,  8,  0, 38,  0, 65,  2,  1, 74, 36, 33, 26, 32, 36,128,
      0, 68,  2,  0, 45, 64,  2,  0,139,148, 32, 16,  0, 32,144,166,
     64, 19,  0, 44, 17,134, 97,  1,128, 65, 16,  2,  4,129, 48, 72,
     72, 32, 40, 80,128, 33,138, 16,  4,  8, 16,  9, 16, 16, 72, 66,
    160, 12,130,146, 96,192, 32,  5,210, 32, 64,  1,  0,  4,  8,130,
     45,130,  2,  0, 72,128, 65, 72, 16,  0,145,  4,  4,  3,132,  0,
    194,  4,104,  0,  0,100,192, 34, 64,  8, 50, 68,  9,134,  0,145,
      2, 40,  1,  0,100, 72,  0, 36, 16,144,  0, 67,  0, 33, 82,134,
     65,139,144, 32, 64, 32,  8,136,  4, 68, 19, 32,  0,  2,132, 96,
    129,144, 36, 64, 48,  0,  8, 16,  8,  8,  2,  1, 16,  4, 32, 67,
    180, 64,144, 18,104,  1,128, 76, 24,  0,  8,192, 18, 73, 64, 16,
     36, 26,  0, 65,137, 36, 76, 16,  0,  4, 82, 16,  9, 74, 32, 65,
     72, 34,105, 17, 20,  8, 16,  6, 36,128,132, 40,  0, 16,  0, 64,
     16,  1,  8, 38,  8, 72,  6, 40,  0, 20,  1, 66,132,  4, 10, 32,
      0,  1,130,  8,  0,130, 36, 18,  4, 64, 64,160, 64,144, 16,  4,
    144, 34, 64, 16, 32, 44,128, 16, 40, 67,  0,  4, 88,  0,  1,129,
     16, 72,  9, 32, 33,131,  4,  0, 66,164, 68,  0,  0,108, 16,160,
     68, 72,128,  0,131,128, 72,201,  0,  0,  0,  2,  5, 16,176,  4,
     19,  4, 41, 16,146, 64,  8,  4, 68,130, 34,  0, 25, 32,  0, 25,
     32,  1,129,144, 96,138,  0, 65,192,  2, 69, 16,  4,  0,  2,162,
      9, 64, 16, 33, 73, 32,  1, 66, 48, 44,  0, 20, 68,  1, 34,  4,
      2,146,  8,137,  4, 33,128, 16,  5,  1, 32, 64, 65,128,  4,  0,
     18,  9, 64,176,100, 88, 50,  1,  8,144,  0, 65,  4,  9,193,128,
     97,  8,144,  0,154,  0, 36,  1, 18,  8,  2, 38,  5,130,  6,  8,
      8,  0, 32, 72, 32,  0, 24, 36, 72,  3,  2,  0, 17,  0,  9,  0,
    132,  1, 74, 16,  1,152,  0,  4, 24,134,  0,192,  0, 32,129,128,
      4, 16, 48,  5,  0,180, 12, 74,130, 41,145,  2, 40,  0, 32, 68,
    192,  0, 44,145,128, 64,  1,162,  0, 18,  4,  9,195, 32,  0,  8,
      2, 12, 16, 34,  4,  0,  0, 44, 17,134,  0,192,  0,  0, 18, 50,
     64,137,128, 64, 64,  2,  5, 80,134, 96,130,164, 96, 10, 18, 77,
    128,144,  8, 18,128,  9,  2, 20, 72,  1, 36, 32,138,  0, 68,144,
      4,  4,  1,  2,  0,209, 18,  0, 10,  4, 64,  0, 50, 33,129, 36,
      8, 25,132, 32,  2,  4,  8,137,128, 36,  2,  2,104, 24,130, 68,
     66,  0, 33, 64,  0, 40,  1,128, 69,130, 32, 64, 17,128, 12,  2,
      0, 36, 64,144,  1, 64, 32, 32, 80, 32, 40, 25,  0, 64,  9, 32,
      8,128,  4, 96, 64,128, 32,  8, 48, 73,  9, 52,  0, 17, 36, 36,
    130,  0, 65,194,  0,  4,146,  2, 36,128,  0, 12,  2,160,  0,  1,
      6, 96, 65,  4, 33,208,  0,  1,  1,  0, 72, 18,132,  4,145, 18,
      8,  0, 36, 68,  0, 18, 65, 24, 38, 12, 65,128,  0, 82,  4, 32,
      9,  0, 36,144, 32, 72, 24,  2,  0,  3,162,  9,208, 20,  0,138,
    132, 37, 74,  0, 32,152, 20, 64,  0,162,  5,  0,  0,  0, 64, 20,
      1, 88, 32, 44,128,132,  0,  9, 32, 32,145,  2,  8,  2,176, 65,
      8, 48,  0,  9, 16,  0, 24,  2, 33,  2,  2,  0,  0, 36, 68,  8,
     18, 96,  0,178, 68, 18,  2, 12,192,128, 64,200, 32,  4, 80, 32,
      5,  0,176,  4, 11,  4, 41, 83,  0, 97, 72, 48,  0,130, 32, 41,
      0, 22,  0, 83, 34, 32, 67, 16, 72,  0,128,  4,210,  0, 64,  0,
    162, 68,  3,128, 41,  0,  4,  8,192,  4,100, 64, 48, 40,  9,132,
     68, 80,128, 33,  2,146,  0,192, 16, 96,136, 34,  8,128,  0,  0,
     24,132,  4,131,150,  0,129, 32,  5,  2,  0, 69,136,132,  0, 81,
     32, 32, 81,134, 65, 75,148,  0,128,  0,  8, 17, 32, 76, 88,128,
      4,  3,  6, 32,137,  0,  5,  8, 34,  5,144,  0, 64,  0,130,  9,
     80,  0,  0,  0,160, 65,194, 32,  8,  0, 22,  8, 64, 38, 33,208,
    144,  8,129,144, 65,  0,  2, 68,  8, 16, 12, 10,134,  9,144,  4,
      0,200,160,  4,  8, 48, 32,137,132,  0, 17, 34, 44, 64,  0,  8,
      2,176,  1, 72,  2,  1,  9, 32,  4,  3,  4,  0,128,  2, 96, 66,
     48, 33, 74, 16, 68,  9,  2,  0,  1, 36,  0, 18,130, 33,128,164,
     32, 16,  2,  4,145,160, 64, 24,  4,  0,  2,  6,105,  9,  0,  5,
     88,  2,  1,  0,  0, 72,  0,  0,  0,  3,146, 32,  0, 52,  1,200,
     32, 72,  8, 48,  8, 66,128, 32,145,144,104,  1,  4, 64, 18,  2,
     97,  0, 18,  8,  1,160,  0, 17,  4, 33, 72,  4, 36,146,  0, 12,
      1,132,  4,  0,  0,  1, 18,150, 64,  1,160, 65,136, 34, 40,136,
      0, 68, 66,128, 36, 18, 20,  1, 66,144, 96, 26, 16,  4,129, 16,
     72,  8,  6, 41,131,  2, 64,  2, 36,100,128, 16,  5,128, 16, 64,
      2,  2,  8, 66,132,  1,  9, 32,  4, 80,  0, 96, 17, 48, 64, 19,
      2,  4,129,  0,  9,  8, 32, 69, 74, 16, 97,144, 38, 12,  8,  2,
     33,145,  0, 96,  2,  4,  0,  2,  0, 12,  8,  6,  8, 72,132,  8,
     17,  2,  0,128,164,  0, 90, 32,  0,136,  4,  4,  2,  0,  9,  0,
     20,  8, 73, 20, 32,200,  0,  4,145,160, 64, 89,128,  0, 18, 16,
      0,128,128,101,  0,  0,  4,  0,128, 64, 25,  0, 33,  3,132, 96,
    192,  4, 36, 26, 18, 97,128,128,  8,  2,  4,  9, 66, 18, 32,  8,
     52,  4,144, 32,  1,  1,160,  0, 11,  0,  8,145,146, 64,  2, 52,
     64,136, 16, 97, 25,  2,  0, 64,  4, 37,192,128,104,  8,  4, 33,
    128, 34,  4,  0,160, 12,  1,132, 32, 65,  0,  8,138,  0, 32,138,
      0, 72,136,  4,  4, 17,130,  8, 64,134,  9, 73,164, 64,  0, 16,
      1,  1,162,  4, 80,128, 12,128,  0, 72,130,160,  1, 24, 18, 65,
      1,  4, 72, 65,  0, 36,  1,  0,  0,136, 20,  0,  2,  0,104,  1,
     32,  8, 74, 34,  8,131,128,  0,137,  4,  1,194,  0,  0,  0, 52,
      4,  0,130, 40,  2,  2, 65, 74,144,  5,130,  2,  9,128, 36,  4,
     65,  0,  1,146,128, 40,  1, 20,  0, 80, 32, 76, 16,176,  4, 67,
    164, 33,144,  4,  1,  2,  0, 68, 72,  0,100,  8,  6,  0, 66, 32,
      8,  2,146,  1, 74,  0, 32, 80, 50, 37,144, 34,  4,  9,  0,  8,
     17,128, 33,  1, 16,  5,  0, 50,  8,136,148,  8,  8, 36, 13,193,
    128, 64, 11, 32, 64, 24, 18,  4,  0, 34, 64, 16, 38,  5,193,130,
      0,  1, 48, 36,  2, 34, 65,  8, 36, 72, 26,  0, 37,210, 18, 40,
     66,  0,  4, 64, 48, 65,  0,  2,  0, 19, 32, 36,209,132,  8,137,
    128,  4, 82,  0, 68, 24,164,  0,  0,  6, 32,145, 16,  9, 66, 32,
     36, 64, 48, 40,  0,132, 64, 64,128,  8, 16,  4,  9,  8,  4, 64,
      8, 34,  0, 25,  2,  0,  0,128, 44,  2,  2, 33,  1,144, 32, 64,
      0, 12,  0, 52, 72, 88, 32,  1, 67,  4, 32,128, 20,  0,144,  0,
    109, 17,  0,  0, 64, 32,  0,  3, 16, 64,136, 48,  5, 74,  0,101,
     16, 36,  8, 24,132, 40,  3,128, 32, 66,176, 64,  0, 16,105, 25,
      4,  0,  0,128,  4,194,  4,  0,  1,  0,  5,  0, 34, 37,  8,150,
      4,  2, 34,  0,208, 16, 41,  1,160, 96,  8, 16,  4,  1, 22, 68,
     16,  2, 40,  2,130, 72, 64,132, 32,144, 34, 40,128,  4,  0, 64,
      4, 36,  0,128, 41,  3, 16, 96, 72,  0,  0,129,160,  0, 81, 32,
     12,209,  0,  1, 65, 32,  4,146,  0,  0, 16,146,  0, 66,  4,  5,
      1,134, 64,128, 16, 32, 82, 32, 33,  0, 16, 72, 10,  2,  0,208,
     18, 65, 72,128,  4,  0,  0, 72,  9, 34,  4,  0, 36,  0, 67, 16,
     96, 10,  0, 68, 18, 32, 44,  8, 32, 68,  0,132,  9, 64,  6,  8,
    193,  0, 64,128, 32,  0,152, 18, 72, 16,162, 32,  0,132, 72,192,
     16, 32,144, 18,  8,152,130,  0, 10,160,  4,  3,  0, 40,195,  0,
     68, 66, 16,  4,  8,  4, 64,  0,  0,  5, 16,  0, 33,  3,128,  4,
    136, 18,105, 16,  0,  4,  8,  4,  4,  2,132, 72, 73,  4, 32, 24,
      2,100,128, 48,  8,  1,  2,  0, 82, 18, 73,  8, 32, 65,136, 16,
     72,  8, 52,  0,  1,134,  5,208,  0,  0,131,132, 33, 64,  2, 65,
     16,128, 72, 64,162, 32, 81,  0,  0, 73,  0,  1,144, 32, 64, 24,
      2, 64,  2, 34,  5, 64,128,  8,130, 16, 32, 24,  0,  5,  1,130,
     64, 88,  0,  4,129,144, 41,  1,160,100,  0, 34, 64,  1,162,  0,
     24,  4, 13,  0,  0, 96,128,148, 96,130, 16, 13,128, 48, 12, 18,
     32,  0,  0, 18, 64,192, 32, 33, 88,  2, 65, 16,128, 68,  3,  2,
      4, 19,144, 41,  8,  0, 68,192,  0, 33,  0, 38,  0, 26,128,  1,
     19, 20, 32, 10, 20, 32,  0, 50, 97,  8,  0, 64, 66, 32,  9,128,
      6,  1,129,128, 96, 66,  0,104,144,130,  8, 66,128,  4,  2,128,
      9, 11,  4,  0,152,  0, 12,129,  6, 68, 72,132, 40,  3,146,  0,
      1,128, 64, 10,  0, 12,129,  2,  8, 81,  4, 40,144,  2, 32,  9,
     16, 96,  0,  0,  9,129,160, 12,  0,164,  9,  0,  2, 40,128, 32,
      0,  2,  2,  4,129, 20,  4,  0,  4,  9, 17, 18, 96, 64, 32,  1,
     72, 48, 64, 17,  0,  8, 10,134,  0,  0,  4, 96,129,  4,  1,208,
      2, 65, 24,144,  0, 10, 32,  0,193,  6,  1,  8,128,100,202, 16,
      4,153,128, 72,  1,130, 32, 80,144, 72,128,132, 32,144, 34,  0,
     25,  0,  4, 24, 32, 36, 16,134, 64,194,  0, 36, 18, 16, 68,  0,
     22,  8, 16, 36,  0, 18,  6,  1,  8,144,  0, 18,  2, 77, 16,128,
     64, 80, 34,  0, 67, 16,  1,  0, 48, 33, 10,  0,  0,  1, 20,  0,
     16,132,  4,193, 16, 41, 10,  0,  1,138,  0, 32,  1, 18, 12, 73,
     32,  4,129,  0, 72,  1,  4, 96,128, 18, 12,  8, 16, 72, 74,  4,
     40, 16,  0, 40, 64,132, 69, 80, 16, 96, 16,  6, 68,  1,128,  9,
      0,134,  1, 66,160,  0,144,  0,  5,144, 34, 64, 65,  0,  8,128,
      2,  8,192,  0,  1, 88, 48, 73,  9, 20,  0, 65,  2, 12,  2,128,
     64,137,  0, 36,  8, 16,  5,144, 50, 64, 10,130,  8,  0, 18, 97,
      0,  4, 33,  0, 34,  4, 16, 36,  8, 10,  4,  1, 16,  0, 32, 64,
    132,  4,136, 34, 32,144, 18,  0, 83,  6, 36,  1,  4, 64, 11, 20,
     96,130,  2, 13, 16,144, 12,  8, 32,  9,  0, 20,  9,128,128, 36,
    130,  0, 64,  1,  2, 68,  1, 32, 12, 64,132, 64, 10, 16, 65,  0,
     48,  5,  9,128, 68,  8, 32, 32,  2,  0, 73, 67, 32, 33,  0, 32,
      0,  1,182,  8, 64,  4,  8,  2,128,  1, 65,128, 64,  8, 16, 36,
      0, 32,  4, 18,134,  9,192, 18, 33,129, 20,  4,  0,  2, 32,137,
    180, 68, 18,128,  0,209,  0,105, 64,128,  0, 66, 18,  0, 24,  4,
      0, 73,  6, 33,  2,  4, 40,  2,132,  1,192, 16,104,  0, 32,  8,
     64,  0,  8,145, 16,  1,129, 36,  4,210, 16, 76,136,134,  0, 16,
    128, 12,  2, 20,  0,138,144, 64, 24, 32, 33,128,164,  0, 88, 36,
     32, 16, 16, 96,193, 48, 65, 72,  2, 72,  9,  0, 64,  9,  2,  5,
     17,130, 32, 74, 32, 36, 24,  2, 12, 16, 34, 12, 10,  4,  0,  3,
      6, 72, 72,  4,  4,  2,  0, 33,128,132,  0, 24,  0, 12,  2, 18,
      1,  0, 20,  5,130, 16, 65,137, 18,  8, 64,164, 33,  1,132, 72,
      2, 16, 96, 64,  2, 40,  0, 20,  8, 64,160, 32, 81, 18,  0,194,
      0,  1, 26, 48, 64,137, 18, 76,  2,128,  0,  0, 20,  1,  1,160,
     33, 24, 34, 33, 24,  6, 64,  1,128,  0,144,  4, 72,  2, 48,  4,
      8,  0,  5,136, 36,  8, 72,  4, 36,  2,  6,  0,128,  0,  0,  0,
     16,101, 17,144,  0, 10,130,  4,195,  4, 96, 72, 36,  4,146,  2,
     68,136,128, 64, 24,  6, 41,128, 16,  1,  0,  0, 68,200, 16, 33,
    137, 48,  0, 75,160,  1, 16, 20,  0,  2,148, 64,  0, 32,101,  0,
    162, 12, 64, 34, 32,129, 18, 32,130,  4,  1, 16,  0,  8,136,  0,
      0, 17,128,  4, 66,128, 64, 65, 20,  0, 64, 50, 44,128, 36,  4,
     25,  0,  0,145,  0, 32,131,  0,  5, 64, 32,  9,  1,132, 64, 64,
     32, 32, 17,  0, 64, 65,144, 32,  0,  0, 64,144,146, 72, 24,  6,
      8,129,128, 72,  1, 52, 36, 16, 32,  4,  0, 32,  4, 24,  6, 45,
    144, 16,  1,  0,144,  0, 10, 34,  1,  0, 34,  0, 17,132,  1,  1,
      0, 32,136,  0, 68,  0, 34,  1,  0,166, 64,  2,  6, 32, 17,  0,
      1,200,160,  4,138,  0, 40, 25,128,  0, 82,160, 36, 18, 18,  9,
      8, 36,  1, 72,  0,  4,  0, 36, 64,  2,132,  8,  0,  4, 72, 64,
    144, 96, 10, 34,  1,136, 20,  8,  1,  2,  8,211,  0, 32,192,144,
     36, 16,  0,  0,  1,176,  8, 10,160,  0,128,  0,  1,  9,  0, 32,
     82,  2, 37,  0, 36,  4,  2,132, 36, 16,146, 64,  2,160, 64,  0,
     34,  8, 17,  4,  8,  1, 34,  0, 66, 20,  0,  9,144, 33,  0, 48,
    108,  0,  0, 12,  0, 34,  9,144, 16, 40, 64,  0, 32,192, 32,  0,
    144,  0, 64,  1,130,  5, 18, 18,  9,193,  4, 97,128,  2, 40,129,
     36,  0, 73,  4,  8, 16,134, 41, 65,128, 33, 10, 48, 73,136,144,
      0, 65,  4, 41,129,128, 65,  9,  0, 64, 18, 16, 64,  0, 16, 64,
     72,  2,  5,128,  2, 33, 64, 32,  0, 88, 32, 96,  0,144, 72,  0,
    128, 40,192,128, 72,  0,  0, 68,128,  2,  0,  9,  6,  0, 18,  2,
      1,  0, 16,  8,131, 16, 69, 18,  0, 44,  8,  4, 68,  0, 32, 32,
    192, 16, 32,  1,  0,  5,200, 32,  4,152, 16,  8, 16,  0, 36,  2,
     22, 64,136,  0, 97,136, 18, 36,128,166,  0, 66,  0,  8, 16,  6,
     72, 64,160,  0, 80, 32,  4,129,164, 64, 24,  0,  8, 16,128,  1
};

/*
 * odd primes < 2^16
 *
 * This table is useful to walk thru 16 bit odd primes to factor a 32 bit
 * value.  Use the pr_map[] array to quickly determine if a 16 bit odd
 * value is prime.
 *
 * We end the list with the value 1.  Thus, loops of the form:
 *
 *      FULL isqr, n;
 *      unsigned short *tp;
 *
 *      for (isqr=fsqrt(n), tp=prime; (*tp <= isqr) && (n % *tp); ++tp) {
 *      }
 *
 * will terminate because *tp == 1 and thus (n % *tp) == 0.  To determine if
 * a factor was found, one must:
 *
 *      if (*tp <= isqr && *tp != 1) {
 *              *tp is a factor of n
 *      }
 */
CONST unsigned short prime[MAP_POPCNT+1] = {
    3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
    79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157,
    163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239,
    241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331,
    337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
    431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509,
    521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613,
    617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709,
    719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821,
    823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919,
    929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
    1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093,
    1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187,
    1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,
    1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367,
    1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453,
    1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543,
    1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613,
    1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709,
    1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801,
    1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901,
    1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999,
    2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087,
    2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179,
    2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281,
    2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371,
    2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447,
    2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557,
    2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671,
    2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731,
    2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833,
    2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927,
    2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037,
    3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163,
    3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253,
    3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343,
    3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457,
    3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539,
    3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623,
    3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719,
    3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823,
    3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919,
    3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019,
    4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127,
    4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229,
    4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327,
    4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441,
    4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523,
    4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643,
    4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733,
    4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861,
    4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957,
    4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039,
    5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153,
    5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273,
    5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393,
    5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477,
    5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569,
    5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669,
    5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783,
    5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861,
    5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987,
    6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091,
    6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203,
    6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299,
    6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
    6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521,
    6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619,
    6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719,
    6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829,
    6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947,
    6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019,
    7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151,
    7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247,
    7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393,
    7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507,
    7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583,
    7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687,
    7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793,
    7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907,
    7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039,
    8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147,
    8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243,
    8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363,
    8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467,
    8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599,
    8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693,
    8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783,
    8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887,
    8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007,
    9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127,
    9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221,
    9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337,
    9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431,
    9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521,
    9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643,
    9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749,
    9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851,
    9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949,
    9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091,
    10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169,
    10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271,
    10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357,
    10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477,
    10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601,
    10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691,
    10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799,
    10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903,
    10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027,
    11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119,
    11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243,
    11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329,
    11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447,
    11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551,
    11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689,
    11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801,
    11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897,
    11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971,
    11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097,
    12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197,
    12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281,
    12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401,
    12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491,
    12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577,
    12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659,
    12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781,
    12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899,
    12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979,
    12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093,
    13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177,
    13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297,
    13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411,
    13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513,
    13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633,
    13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721,
    13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829,
    13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913,
    13921, 13931, 13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033,
    14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159,
    14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303,
    14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411,
    14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519,
    14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621,
    14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717,
    14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783,
    14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887,
    14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013,
    15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121,
    15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227,
    15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307,
    15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391,
    15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497,
    15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 15619,
    15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727,
    15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787, 15791, 15797,
    15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907,
    15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033,
    16057, 16061, 16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111,
    16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231,
    16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363,
    16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477,
    16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603,
    16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693,
    16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 16823, 16829,
    16831, 16843, 16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927, 16931,
    16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 17021, 17027, 17029,
    17033, 17041, 17047, 17053, 17077, 17093, 17099, 17107, 17117, 17123, 17137,
    17159, 17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257,
    17291, 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377,
    17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467,
    17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569,
    17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669,
    17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 17789,
    17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 17891, 17903, 17909,
    17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 17977, 17981, 17987,
    17989, 18013, 18041, 18043, 18047, 18049, 18059, 18061, 18077, 18089, 18097,
    18119, 18121, 18127, 18131, 18133, 18143, 18149, 18169, 18181, 18191, 18199,
    18211, 18217, 18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289,
    18301, 18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397,
    18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493,
    18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617,
    18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749,
    18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 18911,
    18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009, 19013, 19031,
    19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 19139, 19141, 19157,
    19163, 19181, 19183, 19207, 19211, 19213, 19219, 19231, 19237, 19249, 19259,
    19267, 19273, 19289, 19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387,
    19391, 19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457,
    19463, 19469, 19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543,
    19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687,
    19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777,
    19793, 19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 19891,
    19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991, 19993,
    19997, 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 20089, 20101,
    20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 20161, 20173, 20177,
    20183, 20201, 20219, 20231, 20233, 20249, 20261, 20269, 20287, 20297, 20323,
    20327, 20333, 20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399,
    20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521,
    20533, 20543, 20549, 20551, 20563, 20593, 20599, 20611, 20627, 20639, 20641,
    20663, 20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753,
    20759, 20771, 20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879, 20887,
    20897, 20899, 20903, 20921, 20929, 20939, 20947, 20959, 20963, 20981, 20983,
    21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059, 21061, 21067, 21089,
    21101, 21107, 21121, 21139, 21143, 21149, 21157, 21163, 21169, 21179, 21187,
    21191, 21193, 21211, 21221, 21227, 21247, 21269, 21277, 21283, 21313, 21317,
    21319, 21323, 21341, 21347, 21377, 21379, 21383, 21391, 21397, 21401, 21407,
    21419, 21433, 21467, 21481, 21487, 21491, 21493, 21499, 21503, 21517, 21521,
    21523, 21529, 21557, 21559, 21563, 21569, 21577, 21587, 21589, 21599, 21601,
    21611, 21613, 21617, 21647, 21649, 21661, 21673, 21683, 21701, 21713, 21727,
    21737, 21739, 21751, 21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821,
    21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911, 21929, 21937,
    21943, 21961, 21977, 21991, 21997, 22003, 22013, 22027, 22031, 22037, 22039,
    22051, 22063, 22067, 22073, 22079, 22091, 22093, 22109, 22111, 22123, 22129,
    22133, 22147, 22153, 22157, 22159, 22171, 22189, 22193, 22229, 22247, 22259,
    22271, 22273, 22277, 22279, 22283, 22291, 22303, 22307, 22343, 22349, 22367,
    22369, 22381, 22391, 22397, 22409, 22433, 22441, 22447, 22453, 22469, 22481,
    22483, 22501, 22511, 22531, 22541, 22543, 22549, 22567, 22571, 22573, 22613,
    22619, 22621, 22637, 22639, 22643, 22651, 22669, 22679, 22691, 22697, 22699,
    22709, 22717, 22721, 22727, 22739, 22741, 22751, 22769, 22777, 22783, 22787,
    22807, 22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901, 22907, 22921,
    22937, 22943, 22961, 22963, 22973, 22993, 23003, 23011, 23017, 23021, 23027,
    23029, 23039, 23041, 23053, 23057, 23059, 23063, 23071, 23081, 23087, 23099,
    23117, 23131, 23143, 23159, 23167, 23173, 23189, 23197, 23201, 23203, 23209,
    23227, 23251, 23269, 23279, 23291, 23293, 23297, 23311, 23321, 23327, 23333,
    23339, 23357, 23369, 23371, 23399, 23417, 23431, 23447, 23459, 23473, 23497,
    23509, 23531, 23537, 23539, 23549, 23557, 23561, 23563, 23567, 23581, 23593,
    23599, 23603, 23609, 23623, 23627, 23629, 23633, 23663, 23669, 23671, 23677,
    23687, 23689, 23719, 23741, 23743, 23747, 23753, 23761, 23767, 23773, 23789,
    23801, 23813, 23819, 23827, 23831, 23833, 23857, 23869, 23873, 23879, 23887,
    23893, 23899, 23909, 23911, 23917, 23929, 23957, 23971, 23977, 23981, 23993,
    24001, 24007, 24019, 24023, 24029, 24043, 24049, 24061, 24071, 24077, 24083,
    24091, 24097, 24103, 24107, 24109, 24113, 24121, 24133, 24137, 24151, 24169,
    24179, 24181, 24197, 24203, 24223, 24229, 24239, 24247, 24251, 24281, 24317,
    24329, 24337, 24359, 24371, 24373, 24379, 24391, 24407, 24413, 24419, 24421,
    24439, 24443, 24469, 24473, 24481, 24499, 24509, 24517, 24527, 24533, 24547,
    24551, 24571, 24593, 24611, 24623, 24631, 24659, 24671, 24677, 24683, 24691,
    24697, 24709, 24733, 24749, 24763, 24767, 24781, 24793, 24799, 24809, 24821,
    24841, 24847, 24851, 24859, 24877, 24889, 24907, 24917, 24919, 24923, 24943,
    24953, 24967, 24971, 24977, 24979, 24989, 25013, 25031, 25033, 25037, 25057,
    25073, 25087, 25097, 25111, 25117, 25121, 25127, 25147, 25153, 25163, 25169,
    25171, 25183, 25189, 25219, 25229, 25237, 25243, 25247, 25253, 25261, 25301,
    25303, 25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367, 25373, 25391,
    25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463, 25469, 25471, 25523,
    25537, 25541, 25561, 25577, 25579, 25583, 25589, 25601, 25603, 25609, 25621,
    25633, 25639, 25643, 25657, 25667, 25673, 25679, 25693, 25703, 25717, 25733,
    25741, 25747, 25759, 25763, 25771, 25793, 25799, 25801, 25819, 25841, 25847,
    25849, 25867, 25873, 25889, 25903, 25913, 25919, 25931, 25933, 25939, 25943,
    25951, 25969, 25981, 25997, 25999, 26003, 26017, 26021, 26029, 26041, 26053,
    26083, 26099, 26107, 26111, 26113, 26119, 26141, 26153, 26161, 26171, 26177,
    26183, 26189, 26203, 26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267,
    26293, 26297, 26309, 26317, 26321, 26339, 26347, 26357, 26371, 26387, 26393,
    26399, 26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479, 26489, 26497,
    26501, 26513, 26539, 26557, 26561, 26573, 26591, 26597, 26627, 26633, 26641,
    26647, 26669, 26681, 26683, 26687, 26693, 26699, 26701, 26711, 26713, 26717,
    26723, 26729, 26731, 26737, 26759, 26777, 26783, 26801, 26813, 26821, 26833,
    26839, 26849, 26861, 26863, 26879, 26881, 26891, 26893, 26903, 26921, 26927,
    26947, 26951, 26953, 26959, 26981, 26987, 26993, 27011, 27017, 27031, 27043,
    27059, 27061, 27067, 27073, 27077, 27091, 27103, 27107, 27109, 27127, 27143,
    27179, 27191, 27197, 27211, 27239, 27241, 27253, 27259, 27271, 27277, 27281,
    27283, 27299, 27329, 27337, 27361, 27367, 27397, 27407, 27409, 27427, 27431,
    27437, 27449, 27457, 27479, 27481, 27487, 27509, 27527, 27529, 27539, 27541,
    27551, 27581, 27583, 27611, 27617, 27631, 27647, 27653, 27673, 27689, 27691,
    27697, 27701, 27733, 27737, 27739, 27743, 27749, 27751, 27763, 27767, 27773,
    27779, 27791, 27793, 27799, 27803, 27809, 27817, 27823, 27827, 27847, 27851,
    27883, 27893, 27901, 27917, 27919, 27941, 27943, 27947, 27953, 27961, 27967,
    27983, 27997, 28001, 28019, 28027, 28031, 28051, 28057, 28069, 28081, 28087,
    28097, 28099, 28109, 28111, 28123, 28151, 28163, 28181, 28183, 28201, 28211,
    28219, 28229, 28277, 28279, 28283, 28289, 28297, 28307, 28309, 28319, 28349,
    28351, 28387, 28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447, 28463,
    28477, 28493, 28499, 28513, 28517, 28537, 28541, 28547, 28549, 28559, 28571,
    28573, 28579, 28591, 28597, 28603, 28607, 28619, 28621, 28627, 28631, 28643,
    28649, 28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711, 28723, 28729,
    28751, 28753, 28759, 28771, 28789, 28793, 28807, 28813, 28817, 28837, 28843,
    28859, 28867, 28871, 28879, 28901, 28909, 28921, 28927, 28933, 28949, 28961,
    28979, 29009, 29017, 29021, 29023, 29027, 29033, 29059, 29063, 29077, 29101,
    29123, 29129, 29131, 29137, 29147, 29153, 29167, 29173, 29179, 29191, 29201,
    29207, 29209, 29221, 29231, 29243, 29251, 29269, 29287, 29297, 29303, 29311,
    29327, 29333, 29339, 29347, 29363, 29383, 29387, 29389, 29399, 29401, 29411,
    29423, 29429, 29437, 29443, 29453, 29473, 29483, 29501, 29527, 29531, 29537,
    29567, 29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633, 29641, 29663,
    29669, 29671, 29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789, 29803,
    29819, 29833, 29837, 29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921,
    29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029, 30047, 30059, 30071,
    30089, 30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137, 30139, 30161,
    30169, 30181, 30187, 30197, 30203, 30211, 30223, 30241, 30253, 30259, 30269,
    30271, 30293, 30307, 30313, 30319, 30323, 30341, 30347, 30367, 30389, 30391,
    30403, 30427, 30431, 30449, 30467, 30469, 30491, 30493, 30497, 30509, 30517,
    30529, 30539, 30553, 30557, 30559, 30577, 30593, 30631, 30637, 30643, 30649,
    30661, 30671, 30677, 30689, 30697, 30703, 30707, 30713, 30727, 30757, 30763,
    30773, 30781, 30803, 30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859,
    30869, 30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30977,
    30983, 31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079, 31081, 31091,
    31121, 31123, 31139, 31147, 31151, 31153, 31159, 31177, 31181, 31183, 31189,
    31193, 31219, 31223, 31231, 31237, 31247, 31249, 31253, 31259, 31267, 31271,
    31277, 31307, 31319, 31321, 31327, 31333, 31337, 31357, 31379, 31387, 31391,
    31393, 31397, 31469, 31477, 31481, 31489, 31511, 31513, 31517, 31531, 31541,
    31543, 31547, 31567, 31573, 31583, 31601, 31607, 31627, 31643, 31649, 31657,
    31663, 31667, 31687, 31699, 31721, 31723, 31727, 31729, 31741, 31751, 31769,
    31771, 31793, 31799, 31817, 31847, 31849, 31859, 31873, 31883, 31891, 31907,
    31957, 31963, 31973, 31981, 31991, 32003, 32009, 32027, 32029, 32051, 32057,
    32059, 32063, 32069, 32077, 32083, 32089, 32099, 32117, 32119, 32141, 32143,
    32159, 32173, 32183, 32189, 32191, 32203, 32213, 32233, 32237, 32251, 32257,
    32261, 32297, 32299, 32303, 32309, 32321, 32323, 32327, 32341, 32353, 32359,
    32363, 32369, 32371, 32377, 32381, 32401, 32411, 32413, 32423, 32429, 32441,
    32443, 32467, 32479, 32491, 32497, 32503, 32507, 32531, 32533, 32537, 32561,
    32563, 32569, 32573, 32579, 32587, 32603, 32609, 32611, 32621, 32633, 32647,
    32653, 32687, 32693, 32707, 32713, 32717, 32719, 32749, 32771, 32779, 32783,
    32789, 32797, 32801, 32803, 32831, 32833, 32839, 32843, 32869, 32887, 32909,
    32911, 32917, 32933, 32939, 32941, 32957, 32969, 32971, 32983, 32987, 32993,
    32999, 33013, 33023, 33029, 33037, 33049, 33053, 33071, 33073, 33083, 33091,
    33107, 33113, 33119, 33149, 33151, 33161, 33179, 33181, 33191, 33199, 33203,
    33211, 33223, 33247, 33287, 33289, 33301, 33311, 33317, 33329, 33331, 33343,
    33347, 33349, 33353, 33359, 33377, 33391, 33403, 33409, 33413, 33427, 33457,
    33461, 33469, 33479, 33487, 33493, 33503, 33521, 33529, 33533, 33547, 33563,
    33569, 33577, 33581, 33587, 33589, 33599, 33601, 33613, 33617, 33619, 33623,
    33629, 33637, 33641, 33647, 33679, 33703, 33713, 33721, 33739, 33749, 33751,
    33757, 33767, 33769, 33773, 33791, 33797, 33809, 33811, 33827, 33829, 33851,
    33857, 33863, 33871, 33889, 33893, 33911, 33923, 33931, 33937, 33941, 33961,
    33967, 33997, 34019, 34031, 34033, 34039, 34057, 34061, 34123, 34127, 34129,
    34141, 34147, 34157, 34159, 34171, 34183, 34211, 34213, 34217, 34231, 34253,
    34259, 34261, 34267, 34273, 34283, 34297, 34301, 34303, 34313, 34319, 34327,
    34337, 34351, 34361, 34367, 34369, 34381, 34403, 34421, 34429, 34439, 34457,
    34469, 34471, 34483, 34487, 34499, 34501, 34511, 34513, 34519, 34537, 34543,
    34549, 34583, 34589, 34591, 34603, 34607, 34613, 34631, 34649, 34651, 34667,
    34673, 34679, 34687, 34693, 34703, 34721, 34729, 34739, 34747, 34757, 34759,
    34763, 34781, 34807, 34819, 34841, 34843, 34847, 34849, 34871, 34877, 34883,
    34897, 34913, 34919, 34939, 34949, 34961, 34963, 34981, 35023, 35027, 35051,
    35053, 35059, 35069, 35081, 35083, 35089, 35099, 35107, 35111, 35117, 35129,
    35141, 35149, 35153, 35159, 35171, 35201, 35221, 35227, 35251, 35257, 35267,
    35279, 35281, 35291, 35311, 35317, 35323, 35327, 35339, 35353, 35363, 35381,
    35393, 35401, 35407, 35419, 35423, 35437, 35447, 35449, 35461, 35491, 35507,
    35509, 35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573, 35591, 35593,
    35597, 35603, 35617, 35671, 35677, 35729, 35731, 35747, 35753, 35759, 35771,
    35797, 35801, 35803, 35809, 35831, 35837, 35839, 35851, 35863, 35869, 35879,
    35897, 35899, 35911, 35923, 35933, 35951, 35963, 35969, 35977, 35983, 35993,
    35999, 36007, 36011, 36013, 36017, 36037, 36061, 36067, 36073, 36083, 36097,
    36107, 36109, 36131, 36137, 36151, 36161, 36187, 36191, 36209, 36217, 36229,
    36241, 36251, 36263, 36269, 36277, 36293, 36299, 36307, 36313, 36319, 36341,
    36343, 36353, 36373, 36383, 36389, 36433, 36451, 36457, 36467, 36469, 36473,
    36479, 36493, 36497, 36523, 36527, 36529, 36541, 36551, 36559, 36563, 36571,
    36583, 36587, 36599, 36607, 36629, 36637, 36643, 36653, 36671, 36677, 36683,
    36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761, 36767, 36779, 36781,
    36787, 36791, 36793, 36809, 36821, 36833, 36847, 36857, 36871, 36877, 36887,
    36899, 36901, 36913, 36919, 36923, 36929, 36931, 36943, 36947, 36973, 36979,
    36997, 37003, 37013, 37019, 37021, 37039, 37049, 37057, 37061, 37087, 37097,
    37117, 37123, 37139, 37159, 37171, 37181, 37189, 37199, 37201, 37217, 37223,
    37243, 37253, 37273, 37277, 37307, 37309, 37313, 37321, 37337, 37339, 37357,
    37361, 37363, 37369, 37379, 37397, 37409, 37423, 37441, 37447, 37463, 37483,
    37489, 37493, 37501, 37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561,
    37567, 37571, 37573, 37579, 37589, 37591, 37607, 37619, 37633, 37643, 37649,
    37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781, 37783, 37799, 37811,
    37813, 37831, 37847, 37853, 37861, 37871, 37879, 37889, 37897, 37907, 37951,
    37957, 37963, 37967, 37987, 37991, 37993, 37997, 38011, 38039, 38047, 38053,
    38069, 38083, 38113, 38119, 38149, 38153, 38167, 38177, 38183, 38189, 38197,
    38201, 38219, 38231, 38237, 38239, 38261, 38273, 38281, 38287, 38299, 38303,
    38317, 38321, 38327, 38329, 38333, 38351, 38371, 38377, 38393, 38431, 38447,
    38449, 38453, 38459, 38461, 38501, 38543, 38557, 38561, 38567, 38569, 38593,
    38603, 38609, 38611, 38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693,
    38699, 38707, 38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767, 38783,
    38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873, 38891, 38903,
    38917, 38921, 38923, 38933, 38953, 38959, 38971, 38977, 38993, 39019, 39023,
    39041, 39043, 39047, 39079, 39089, 39097, 39103, 39107, 39113, 39119, 39133,
    39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209, 39217, 39227, 39229,
    39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323, 39341, 39343,
    39359, 39367, 39371, 39373, 39383, 39397, 39409, 39419, 39439, 39443, 39451,
    39461, 39499, 39503, 39509, 39511, 39521, 39541, 39551, 39563, 39569, 39581,
    39607, 39619, 39623, 39631, 39659, 39667, 39671, 39679, 39703, 39709, 39719,
    39727, 39733, 39749, 39761, 39769, 39779, 39791, 39799, 39821, 39827, 39829,
    39839, 39841, 39847, 39857, 39863, 39869, 39877, 39883, 39887, 39901, 39929,
    39937, 39953, 39971, 39979, 39983, 39989, 40009, 40013, 40031, 40037, 40039,
    40063, 40087, 40093, 40099, 40111, 40123, 40127, 40129, 40151, 40153, 40163,
    40169, 40177, 40189, 40193, 40213, 40231, 40237, 40241, 40253, 40277, 40283,
    40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427, 40429, 40433, 40459,
    40471, 40483, 40487, 40493, 40499, 40507, 40519, 40529, 40531, 40543, 40559,
    40577, 40583, 40591, 40597, 40609, 40627, 40637, 40639, 40693, 40697, 40699,
    40709, 40739, 40751, 40759, 40763, 40771, 40787, 40801, 40813, 40819, 40823,
    40829, 40841, 40847, 40849, 40853, 40867, 40879, 40883, 40897, 40903, 40927,
    40933, 40939, 40949, 40961, 40973, 40993, 41011, 41017, 41023, 41039, 41047,
    41051, 41057, 41077, 41081, 41113, 41117, 41131, 41141, 41143, 41149, 41161,
    41177, 41179, 41183, 41189, 41201, 41203, 41213, 41221, 41227, 41231, 41233,
    41243, 41257, 41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381,
    41387, 41389, 41399, 41411, 41413, 41443, 41453, 41467, 41479, 41491, 41507,
    41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593, 41597, 41603, 41609,
    41611, 41617, 41621, 41627, 41641, 41647, 41651, 41659, 41669, 41681, 41687,
    41719, 41729, 41737, 41759, 41761, 41771, 41777, 41801, 41809, 41813, 41843,
    41849, 41851, 41863, 41879, 41887, 41893, 41897, 41903, 41911, 41927, 41941,
    41947, 41953, 41957, 41959, 41969, 41981, 41983, 41999, 42013, 42017, 42019,
    42023, 42043, 42061, 42071, 42073, 42083, 42089, 42101, 42131, 42139, 42157,
    42169, 42179, 42181, 42187, 42193, 42197, 42209, 42221, 42223, 42227, 42239,
    42257, 42281, 42283, 42293, 42299, 42307, 42323, 42331, 42337, 42349, 42359,
    42373, 42379, 42391, 42397, 42403, 42407, 42409, 42433, 42437, 42443, 42451,
    42457, 42461, 42463, 42467, 42473, 42487, 42491, 42499, 42509, 42533, 42557,
    42569, 42571, 42577, 42589, 42611, 42641, 42643, 42649, 42667, 42677, 42683,
    42689, 42697, 42701, 42703, 42709, 42719, 42727, 42737, 42743, 42751, 42767,
    42773, 42787, 42793, 42797, 42821, 42829, 42839, 42841, 42853, 42859, 42863,
    42899, 42901, 42923, 42929, 42937, 42943, 42953, 42961, 42967, 42979, 42989,
    43003, 43013, 43019, 43037, 43049, 43051, 43063, 43067, 43093, 43103, 43117,
    43133, 43151, 43159, 43177, 43189, 43201, 43207, 43223, 43237, 43261, 43271,
    43283, 43291, 43313, 43319, 43321, 43331, 43391, 43397, 43399, 43403, 43411,
    43427, 43441, 43451, 43457, 43481, 43487, 43499, 43517, 43541, 43543, 43573,
    43577, 43579, 43591, 43597, 43607, 43609, 43613, 43627, 43633, 43649, 43651,
    43661, 43669, 43691, 43711, 43717, 43721, 43753, 43759, 43777, 43781, 43783,
    43787, 43789, 43793, 43801, 43853, 43867, 43889, 43891, 43913, 43933, 43943,
    43951, 43961, 43963, 43969, 43973, 43987, 43991, 43997, 44017, 44021, 44027,
    44029, 44041, 44053, 44059, 44071, 44087, 44089, 44101, 44111, 44119, 44123,
    44129, 44131, 44159, 44171, 44179, 44189, 44201, 44203, 44207, 44221, 44249,
    44257, 44263, 44267, 44269, 44273, 44279, 44281, 44293, 44351, 44357, 44371,
    44381, 44383, 44389, 44417, 44449, 44453, 44483, 44491, 44497, 44501, 44507,
    44519, 44531, 44533, 44537, 44543, 44549, 44563, 44579, 44587, 44617, 44621,
    44623, 44633, 44641, 44647, 44651, 44657, 44683, 44687, 44699, 44701, 44711,
    44729, 44741, 44753, 44771, 44773, 44777, 44789, 44797, 44809, 44819, 44839,
    44843, 44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927, 44939, 44953,
    44959, 44963, 44971, 44983, 44987, 45007, 45013, 45053, 45061, 45077, 45083,
    45119, 45121, 45127, 45131, 45137, 45139, 45161, 45179, 45181, 45191, 45197,
    45233, 45247, 45259, 45263, 45281, 45289, 45293, 45307, 45317, 45319, 45329,
    45337, 45341, 45343, 45361, 45377, 45389, 45403, 45413, 45427, 45433, 45439,
    45481, 45491, 45497, 45503, 45523, 45533, 45541, 45553, 45557, 45569, 45587,
    45589, 45599, 45613, 45631, 45641, 45659, 45667, 45673, 45677, 45691, 45697,
    45707, 45737, 45751, 45757, 45763, 45767, 45779, 45817, 45821, 45823, 45827,
    45833, 45841, 45853, 45863, 45869, 45887, 45893, 45943, 45949, 45953, 45959,
    45971, 45979, 45989, 46021, 46027, 46049, 46051, 46061, 46073, 46091, 46093,
    46099, 46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183, 46187, 46199,
    46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301, 46307, 46309, 46327,
    46337, 46349, 46351, 46381, 46399, 46411, 46439, 46441, 46447, 46451, 46457,
    46471, 46477, 46489, 46499, 46507, 46511, 46523, 46549, 46559, 46567, 46573,
    46589, 46591, 46601, 46619, 46633, 46639, 46643, 46649, 46663, 46679, 46681,
    46687, 46691, 46703, 46723, 46727, 46747, 46751, 46757, 46769, 46771, 46807,
    46811, 46817, 46819, 46829, 46831, 46853, 46861, 46867, 46877, 46889, 46901,
    46919, 46933, 46957, 46993, 46997, 47017, 47041, 47051, 47057, 47059, 47087,
    47093, 47111, 47119, 47123, 47129, 47137, 47143, 47147, 47149, 47161, 47189,
    47207, 47221, 47237, 47251, 47269, 47279, 47287, 47293, 47297, 47303, 47309,
    47317, 47339, 47351, 47353, 47363, 47381, 47387, 47389, 47407, 47417, 47419,
    47431, 47441, 47459, 47491, 47497, 47501, 47507, 47513, 47521, 47527, 47533,
    47543, 47563, 47569, 47581, 47591, 47599, 47609, 47623, 47629, 47639, 47653,
    47657, 47659, 47681, 47699, 47701, 47711, 47713, 47717, 47737, 47741, 47743,
    47777, 47779, 47791, 47797, 47807, 47809, 47819, 47837, 47843, 47857, 47869,
    47881, 47903, 47911, 47917, 47933, 47939, 47947, 47951, 47963, 47969, 47977,
    47981, 48017, 48023, 48029, 48049, 48073, 48079, 48091, 48109, 48119, 48121,
    48131, 48157, 48163, 48179, 48187, 48193, 48197, 48221, 48239, 48247, 48259,
    48271, 48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383, 48397,
    48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487, 48491,
    48497, 48523, 48527, 48533, 48539, 48541, 48563, 48571, 48589, 48593, 48611,
    48619, 48623, 48647, 48649, 48661, 48673, 48677, 48679, 48731, 48733, 48751,
    48757, 48761, 48767, 48779, 48781, 48787, 48799, 48809, 48817, 48821, 48823,
    48847, 48857, 48859, 48869, 48871, 48883, 48889, 48907, 48947, 48953, 48973,
    48989, 48991, 49003, 49009, 49019, 49031, 49033, 49037, 49043, 49057, 49069,
    49081, 49103, 49109, 49117, 49121, 49123, 49139, 49157, 49169, 49171, 49177,
    49193, 49199, 49201, 49207, 49211, 49223, 49253, 49261, 49277, 49279, 49297,
    49307, 49331, 49333, 49339, 49363, 49367, 49369, 49391, 49393, 49409, 49411,
    49417, 49429, 49433, 49451, 49459, 49463, 49477, 49481, 49499, 49523, 49529,
    49531, 49537, 49547, 49549, 49559, 49597, 49603, 49613, 49627, 49633, 49639,
    49663, 49667, 49669, 49681, 49697, 49711, 49727, 49739, 49741, 49747, 49757,
    49783, 49787, 49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853, 49871,
    49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 49957, 49991, 49993,
    49999, 50021, 50023, 50033, 50047, 50051, 50053, 50069, 50077, 50087, 50093,
    50101, 50111, 50119, 50123, 50129, 50131, 50147, 50153, 50159, 50177, 50207,
    50221, 50227, 50231, 50261, 50263, 50273, 50287, 50291, 50311, 50321, 50329,
    50333, 50341, 50359, 50363, 50377, 50383, 50387, 50411, 50417, 50423, 50441,
    50459, 50461, 50497, 50503, 50513, 50527, 50539, 50543, 50549, 50551, 50581,
    50587, 50591, 50593, 50599, 50627, 50647, 50651, 50671, 50683, 50707, 50723,
    50741, 50753, 50767, 50773, 50777, 50789, 50821, 50833, 50839, 50849, 50857,
    50867, 50873, 50891, 50893, 50909, 50923, 50929, 50951, 50957, 50969, 50971,
    50989, 50993, 51001, 51031, 51043, 51047, 51059, 51061, 51071, 51109, 51131,
    51133, 51137, 51151, 51157, 51169, 51193, 51197, 51199, 51203, 51217, 51229,
    51239, 51241, 51257, 51263, 51283, 51287, 51307, 51329, 51341, 51343, 51347,
    51349, 51361, 51383, 51407, 51413, 51419, 51421, 51427, 51431, 51437, 51439,
    51449, 51461, 51473, 51479, 51481, 51487, 51503, 51511, 51517, 51521, 51539,
    51551, 51563, 51577, 51581, 51593, 51599, 51607, 51613, 51631, 51637, 51647,
    51659, 51673, 51679, 51683, 51691, 51713, 51719, 51721, 51749, 51767, 51769,
    51787, 51797, 51803, 51817, 51827, 51829, 51839, 51853, 51859, 51869, 51871,
    51893, 51899, 51907, 51913, 51929, 51941, 51949, 51971, 51973, 51977, 51991,
    52009, 52021, 52027, 52051, 52057, 52067, 52069, 52081, 52103, 52121, 52127,
    52147, 52153, 52163, 52177, 52181, 52183, 52189, 52201, 52223, 52237, 52249,
    52253, 52259, 52267, 52289, 52291, 52301, 52313, 52321, 52361, 52363, 52369,
    52379, 52387, 52391, 52433, 52453, 52457, 52489, 52501, 52511, 52517, 52529,
    52541, 52543, 52553, 52561, 52567, 52571, 52579, 52583, 52609, 52627, 52631,
    52639, 52667, 52673, 52691, 52697, 52709, 52711, 52721, 52727, 52733, 52747,
    52757, 52769, 52783, 52807, 52813, 52817, 52837, 52859, 52861, 52879, 52883,
    52889, 52901, 52903, 52919, 52937, 52951, 52957, 52963, 52967, 52973, 52981,
    52999, 53003, 53017, 53047, 53051, 53069, 53077, 53087, 53089, 53093, 53101,
    53113, 53117, 53129, 53147, 53149, 53161, 53171, 53173, 53189, 53197, 53201,
    53231, 53233, 53239, 53267, 53269, 53279, 53281, 53299, 53309, 53323, 53327,
    53353, 53359, 53377, 53381, 53401, 53407, 53411, 53419, 53437, 53441, 53453,
    53479, 53503, 53507, 53527, 53549, 53551, 53569, 53591, 53593, 53597, 53609,
    53611, 53617, 53623, 53629, 53633, 53639, 53653, 53657, 53681, 53693, 53699,
    53717, 53719, 53731, 53759, 53773, 53777, 53783, 53791, 53813, 53819, 53831,
    53849, 53857, 53861, 53881, 53887, 53891, 53897, 53899, 53917, 53923, 53927,
    53939, 53951, 53959, 53987, 53993, 54001, 54011, 54013, 54037, 54049, 54059,
    54083, 54091, 54101, 54121, 54133, 54139, 54151, 54163, 54167, 54181, 54193,
    54217, 54251, 54269, 54277, 54287, 54293, 54311, 54319, 54323, 54331, 54347,
    54361, 54367, 54371, 54377, 54401, 54403, 54409, 54413, 54419, 54421, 54437,
    54443, 54449, 54469, 54493, 54497, 54499, 54503, 54517, 54521, 54539, 54541,
    54547, 54559, 54563, 54577, 54581, 54583, 54601, 54617, 54623, 54629, 54631,
    54647, 54667, 54673, 54679, 54709, 54713, 54721, 54727, 54751, 54767, 54773,
    54779, 54787, 54799, 54829, 54833, 54851, 54869, 54877, 54881, 54907, 54917,
    54919, 54941, 54949, 54959, 54973, 54979, 54983, 55001, 55009, 55021, 55049,
    55051, 55057, 55061, 55073, 55079, 55103, 55109, 55117, 55127, 55147, 55163,
    55171, 55201, 55207, 55213, 55217, 55219, 55229, 55243, 55249, 55259, 55291,
    55313, 55331, 55333, 55337, 55339, 55343, 55351, 55373, 55381, 55399, 55411,
    55439, 55441, 55457, 55469, 55487, 55501, 55511, 55529, 55541, 55547, 55579,
    55589, 55603, 55609, 55619, 55621, 55631, 55633, 55639, 55661, 55663, 55667,
    55673, 55681, 55691, 55697, 55711, 55717, 55721, 55733, 55763, 55787, 55793,
    55799, 55807, 55813, 55817, 55819, 55823, 55829, 55837, 55843, 55849, 55871,
    55889, 55897, 55901, 55903, 55921, 55927, 55931, 55933, 55949, 55967, 55987,
    55997, 56003, 56009, 56039, 56041, 56053, 56081, 56087, 56093, 56099, 56101,
    56113, 56123, 56131, 56149, 56167, 56171, 56179, 56197, 56207, 56209, 56237,
    56239, 56249, 56263, 56267, 56269, 56299, 56311, 56333, 56359, 56369, 56377,
    56383, 56393, 56401, 56417, 56431, 56437, 56443, 56453, 56467, 56473, 56477,
    56479, 56489, 56501, 56503, 56509, 56519, 56527, 56531, 56533, 56543, 56569,
    56591, 56597, 56599, 56611, 56629, 56633, 56659, 56663, 56671, 56681, 56687,
    56701, 56711, 56713, 56731, 56737, 56747, 56767, 56773, 56779, 56783, 56807,
    56809, 56813, 56821, 56827, 56843, 56857, 56873, 56891, 56893, 56897, 56909,
    56911, 56921, 56923, 56929, 56941, 56951, 56957, 56963, 56983, 56989, 56993,
    56999, 57037, 57041, 57047, 57059, 57073, 57077, 57089, 57097, 57107, 57119,
    57131, 57139, 57143, 57149, 57163, 57173, 57179, 57191, 57193, 57203, 57221,
    57223, 57241, 57251, 57259, 57269, 57271, 57283, 57287, 57301, 57329, 57331,
    57347, 57349, 57367, 57373, 57383, 57389, 57397, 57413, 57427, 57457, 57467,
    57487, 57493, 57503, 57527, 57529, 57557, 57559, 57571, 57587, 57593, 57601,
    57637, 57641, 57649, 57653, 57667, 57679, 57689, 57697, 57709, 57713, 57719,
    57727, 57731, 57737, 57751, 57773, 57781, 57787, 57791, 57793, 57803, 57809,
    57829, 57839, 57847, 57853, 57859, 57881, 57899, 57901, 57917, 57923, 57943,
    57947, 57973, 57977, 57991, 58013, 58027, 58031, 58043, 58049, 58057, 58061,
    58067, 58073, 58099, 58109, 58111, 58129, 58147, 58151, 58153, 58169, 58171,
    58189, 58193, 58199, 58207, 58211, 58217, 58229, 58231, 58237, 58243, 58271,
    58309, 58313, 58321, 58337, 58363, 58367, 58369, 58379, 58391, 58393, 58403,
    58411, 58417, 58427, 58439, 58441, 58451, 58453, 58477, 58481, 58511, 58537,
    58543, 58549, 58567, 58573, 58579, 58601, 58603, 58613, 58631, 58657, 58661,
    58679, 58687, 58693, 58699, 58711, 58727, 58733, 58741, 58757, 58763, 58771,
    58787, 58789, 58831, 58889, 58897, 58901, 58907, 58909, 58913, 58921, 58937,
    58943, 58963, 58967, 58979, 58991, 58997, 59009, 59011, 59021, 59023, 59029,
    59051, 59053, 59063, 59069, 59077, 59083, 59093, 59107, 59113, 59119, 59123,
    59141, 59149, 59159, 59167, 59183, 59197, 59207, 59209, 59219, 59221, 59233,
    59239, 59243, 59263, 59273, 59281, 59333, 59341, 59351, 59357, 59359, 59369,
    59377, 59387, 59393, 59399, 59407, 59417, 59419, 59441, 59443, 59447, 59453,
    59467, 59471, 59473, 59497, 59509, 59513, 59539, 59557, 59561, 59567, 59581,
    59611, 59617, 59621, 59627, 59629, 59651, 59659, 59663, 59669, 59671, 59693,
    59699, 59707, 59723, 59729, 59743, 59747, 59753, 59771, 59779, 59791, 59797,
    59809, 59833, 59863, 59879, 59887, 59921, 59929, 59951, 59957, 59971, 59981,
    59999, 60013, 60017, 60029, 60037, 60041, 60077, 60083, 60089, 60091, 60101,
    60103, 60107, 60127, 60133, 60139, 60149, 60161, 60167, 60169, 60209, 60217,
    60223, 60251, 60257, 60259, 60271, 60289, 60293, 60317, 60331, 60337, 60343,
    60353, 60373, 60383, 60397, 60413, 60427, 60443, 60449, 60457, 60493, 60497,
    60509, 60521, 60527, 60539, 60589, 60601, 60607, 60611, 60617, 60623, 60631,
    60637, 60647, 60649, 60659, 60661, 60679, 60689, 60703, 60719, 60727, 60733,
    60737, 60757, 60761, 60763, 60773, 60779, 60793, 60811, 60821, 60859, 60869,
    60887, 60889, 60899, 60901, 60913, 60917, 60919, 60923, 60937, 60943, 60953,
    60961, 61001, 61007, 61027, 61031, 61043, 61051, 61057, 61091, 61099, 61121,
    61129, 61141, 61151, 61153, 61169, 61211, 61223, 61231, 61253, 61261, 61283,
    61291, 61297, 61331, 61333, 61339, 61343, 61357, 61363, 61379, 61381, 61403,
    61409, 61417, 61441, 61463, 61469, 61471, 61483, 61487, 61493, 61507, 61511,
    61519, 61543, 61547, 61553, 61559, 61561, 61583, 61603, 61609, 61613, 61627,
    61631, 61637, 61643, 61651, 61657, 61667, 61673, 61681, 61687, 61703, 61717,
    61723, 61729, 61751, 61757, 61781, 61813, 61819, 61837, 61843, 61861, 61871,
    61879, 61909, 61927, 61933, 61949, 61961, 61967, 61979, 61981, 61987, 61991,
    62003, 62011, 62017, 62039, 62047, 62053, 62057, 62071, 62081, 62099, 62119,
    62129, 62131, 62137, 62141, 62143, 62171, 62189, 62191, 62201, 62207, 62213,
    62219, 62233, 62273, 62297, 62299, 62303, 62311, 62323, 62327, 62347, 62351,
    62383, 62401, 62417, 62423, 62459, 62467, 62473, 62477, 62483, 62497, 62501,
    62507, 62533, 62539, 62549, 62563, 62581, 62591, 62597, 62603, 62617, 62627,
    62633, 62639, 62653, 62659, 62683, 62687, 62701, 62723, 62731, 62743, 62753,
    62761, 62773, 62791, 62801, 62819, 62827, 62851, 62861, 62869, 62873, 62897,
    62903, 62921, 62927, 62929, 62939, 62969, 62971, 62981, 62983, 62987, 62989,
    63029, 63031, 63059, 63067, 63073, 63079, 63097, 63103, 63113, 63127, 63131,
    63149, 63179, 63197, 63199, 63211, 63241, 63247, 63277, 63281, 63299, 63311,
    63313, 63317, 63331, 63337, 63347, 63353, 63361, 63367, 63377, 63389, 63391,
    63397, 63409, 63419, 63421, 63439, 63443, 63463, 63467, 63473, 63487, 63493,
    63499, 63521, 63527, 63533, 63541, 63559, 63577, 63587, 63589, 63599, 63601,
    63607, 63611, 63617, 63629, 63647, 63649, 63659, 63667, 63671, 63689, 63691,
    63697, 63703, 63709, 63719, 63727, 63737, 63743, 63761, 63773, 63781, 63793,
    63799, 63803, 63809, 63823, 63839, 63841, 63853, 63857, 63863, 63901, 63907,
    63913, 63929, 63949, 63977, 63997, 64007, 64013, 64019, 64033, 64037, 64063,
    64067, 64081, 64091, 64109, 64123, 64151, 64153, 64157, 64171, 64187, 64189,
    64217, 64223, 64231, 64237, 64271, 64279, 64283, 64301, 64303, 64319, 64327,
    64333, 64373, 64381, 64399, 64403, 64433, 64439, 64451, 64453, 64483, 64489,
    64499, 64513, 64553, 64567, 64577, 64579, 64591, 64601, 64609, 64613, 64621,
    64627, 64633, 64661, 64663, 64667, 64679, 64693, 64709, 64717, 64747, 64763,
    64781, 64783, 64793, 64811, 64817, 64849, 64853, 64871, 64877, 64879, 64891,
    64901, 64919, 64921, 64927, 64937, 64951, 64969, 64997, 65003, 65011, 65027,
    65029, 65033, 65053, 65063, 65071, 65089, 65099, 65101, 65111, 65119, 65123,
    65129, 65141, 65147, 65167, 65171, 65173, 65179, 65183, 65203, 65213, 65239,
    65257, 65267, 65269, 65287, 65293, 65309, 65323, 65327, 65353, 65357, 65371,
    65381, 65393, 65407, 65413, 65419, 65423, 65437, 65447, 65449, 65479, 65497,
    65519, 65521, 1
};

/*
 * smallest prime > MAX_SM_PRIME (2^32-5) == 2^32+15
 */
#if BASEB == 32
STATIC CONST HALF _nxt_prime_val_[] = { 0xf, 0x1 };
ZVALUE CONST _nxt_prime_ = { (HALF *)_nxt_prime_val_, 2, 0 };
NUMBER _nxtprime_ = {{(HALF *)_nxt_prime_val_,2,0}, {_oneval_,1,0}, 1, NULL};
#else
STATIC CONST HALF _nxt_prime_val_[] = { 0xf, 0x0, 0x1 };
ZVALUE CONST _nxt_prime_ = { (HALF *)_nxt_prime_val_, 3, 0 };
NUMBER _nxtprime_ = {{(HALF *)_nxt_prime_val_,3,0}, {_oneval_,1,0}, 1, NULL};
#endif

/*
 * JMPMOD*2 as a ZVALUE
 */
STATIC CONST HALF _jmpmod2_val_[] = { JMPMOD*2 };
CONST ZVALUE _jmpmod2_ = { (HALF *)_jmpmod2_val_, 1, 0 };