No25_Maths_3_19.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No |The Chosen Number| Σ(1/p) >= lnlnx-ln2 | Validation\n",
      "--------------------------------------------------------\n",
      "0) | For number: 497 | 2.09471 >= 1.132787 | True\n",
      "1) | For number: 693 | 2.14690 >= 1.184947 | True\n",
      "2) | For number: 633 | 2.13181 >= 1.171006 | True\n",
      "3) | For number: 325 | 2.02568 >= 1.061918 | True\n",
      "4) | For number: 735 | 2.15387 >= 1.193903 | True\n",
      "5) | For number: 810 | 2.16689 >= 1.208518 | True\n",
      "6) | For number: 769 | 2.16184 >= 1.200731 | True\n",
      "7) | For number: 600 | 2.12204 >= 1.162671 | True\n",
      "8) | For number: 766 | 2.16054 >= 1.200143 | True\n",
      "9) | For number: 733 | 2.15387 >= 1.193490 | True\n",
      "10) | For number: 179 | 1.92299 >= 0.953083 | True\n",
      "11) | For number: 849 | 2.17417 >= 1.215515 | True\n",
      "12) | For number: 979 | 2.19505 >= 1.236420 | True\n",
      "13) | For number: 455 | 2.07987 >= 1.118464 | True\n",
      "14) | For number: 867 | 2.17883 >= 1.218621 | True\n",
      "15) | For number: 283 | 2.00944 >= 1.037702 | True\n",
      "16) | For number: 834 | 2.17297 >= 1.212868 | True\n",
      "17) | For number: 156 | 1.89313 >= 0.926213 | True\n",
      "18) | For number: 372 | 2.04576 >= 1.085002 | True\n",
      "19) | For number: 477 | 2.08853 >= 1.126149 | True\n",
      "20) | For number: 494 | 2.09471 >= 1.131811 | True\n",
      "21) | For number: 487 | 2.09267 >= 1.129507 | True\n",
      "22) | For number: 214 | 1.95377 >= 0.986931 | True\n",
      "23) | For number: 788 | 2.16440 >= 1.204397 | True\n",
      "24) | For number: 582 | 2.11698 >= 1.157898 | True\n",
      "25) | For number: 721 | 2.15113 >= 1.190985 | True\n",
      "26) | For number: 608 | 2.12535 >= 1.164739 | True\n",
      "27) | For number: 826 | 2.17056 >= 1.211434 | True\n",
      "28) | For number: 227 | 1.96266 >= 0.997862 | True\n",
      "29) | For number: 151 | 1.89313 >= 0.919741 | True\n",
      "30) | For number: 129 | 1.85767 >= 0.887853 | True\n",
      "31) | For number: 608 | 2.12535 >= 1.164739 | True\n",
      "32) | For number: 206 | 1.94903 >= 0.979806 | True\n",
      "33) | For number: 930 | 2.18773 >= 1.228936 | True\n",
      "34) | For number: 471 | 2.08853 >= 1.124095 | True\n",
      "35) | For number: 768 | 2.16054 >= 1.200535 | True\n",
      "36) | For number: 836 | 2.17297 >= 1.213224 | True\n",
      "37) | For number: 752 | 2.15790 >= 1.197361 | True\n",
      "38) | For number: 247 | 1.97966 >= 1.013306 | True\n",
      "39) | For number: 859 | 2.17767 >= 1.217250 | True\n",
      "40) | For number: 285 | 2.00944 >= 1.038949 | True\n",
      "41) | For number: 627 | 2.13022 >= 1.169528 | True\n",
      "42) | For number: 780 | 2.16313 >= 1.202866 | True\n",
      "43) | For number: 780 | 2.16313 >= 1.202866 | True\n",
      "44) | For number: 688 | 2.14546 >= 1.183840 | True\n",
      "45) | For number: 203 | 1.94903 >= 0.977048 | True\n",
      "46) | For number: 231 | 1.96703 >= 1.001076 | True\n",
      "47) | For number: 251 | 1.98364 >= 1.016218 | True\n",
      "48) | For number: 200 | 1.94903 >= 0.974242 | True\n",
      "49) | For number: 191 | 1.93375 >= 0.965514 | True\n",
      "50) | For number: 123 | 1.84980 >= 0.878004 | True\n",
      "51) | For number: 324 | 2.02568 >= 1.061385 | True\n",
      "52) | For number: 435 | 2.07311 >= 1.111092 | True\n",
      "53) | For number: 490 | 2.09267 >= 1.130499 | True\n",
      "54) | For number: 415 | 2.06372 >= 1.103314 | True\n",
      "55) | For number: 191 | 1.93375 >= 0.965514 | True\n",
      "56) | For number: 317 | 2.02568 >= 1.057600 | True\n",
      "57) | For number: 622 | 2.13022 >= 1.168284 | True\n",
      "58) | For number: 994 | 2.19708 >= 1.238626 | True\n",
      "59) | For number: 589 | 2.11869 >= 1.159774 | True\n",
      "60) | For number: 566 | 2.11174 >= 1.153510 | True\n",
      "61) | For number: 989 | 2.19607 >= 1.237895 | True\n",
      "62) | For number: 357 | 2.04025 >= 1.078024 | True\n",
      "63) | For number: 342 | 2.03167 >= 1.070695 | True\n",
      "64) | For number: 240 | 1.97551 >= 1.008075 | True\n",
      "65) | For number: 811 | 2.16813 >= 1.208702 | True\n",
      "66) | For number: 782 | 2.16313 >= 1.203251 | True\n",
      "67) | For number: 674 | 2.14252 >= 1.180688 | True\n",
      "68) | For number: 691 | 2.14690 >= 1.184506 | True\n",
      "69) | For number: 310 | 2.01611 >= 1.053715 | True\n",
      "70) | For number: 785 | 2.16313 >= 1.203825 | True\n",
      "71) | For number: 538 | 2.10449 >= 1.145473 | True\n",
      "72) | For number: 281 | 2.00591 >= 1.036445 | True\n",
      "73) | For number: 221 | 1.95377 >= 0.992911 | True\n",
      "74) | For number: 315 | 2.02252 >= 1.056500 | True\n",
      "75) | For number: 988 | 2.19607 >= 1.237748 | True\n",
      "76) | For number: 251 | 1.98364 >= 1.016218 | True\n",
      "77) | For number: 694 | 2.14690 >= 1.185168 | True\n",
      "78) | For number: 427 | 2.06848 >= 1.108032 | True\n",
      "79) | For number: 723 | 2.15113 >= 1.191406 | True\n",
      "80) | For number: 778 | 2.16313 >= 1.202481 | True\n",
      "81) | For number: 947 | 2.19091 >= 1.231583 | True\n",
      "82) | For number: 573 | 2.11525 >= 1.155447 | True\n",
      "83) | For number: 715 | 2.14974 >= 1.189714 | True\n",
      "84) | For number: 675 | 2.14252 >= 1.180916 | True\n",
      "85) | For number: 355 | 2.04025 >= 1.077068 | True\n",
      "86) | For number: 105 | 1.82243 >= 0.844571 | True\n",
      "87) | For number: 295 | 2.01286 >= 1.045031 | True\n",
      "88) | For number: 280 | 2.00235 >= 1.035813 | True\n",
      "89) | For number: 203 | 1.94903 >= 0.977048 | True\n",
      "90) | For number: 965 | 2.19196 >= 1.234327 | True\n",
      "91) | For number: 979 | 2.19505 >= 1.236420 | True\n",
      "92) | For number: 409 | 2.06372 >= 1.100896 | True\n",
      "93) | For number: 264 | 1.99133 >= 1.025315 | True\n",
      "94) | For number: 754 | 2.15790 >= 1.197762 | True\n",
      "95) | For number: 355 | 2.04025 >= 1.077068 | True\n",
      "96) | For number: 273 | 1.99874 >= 1.031309 | True\n",
      "97) | For number: 132 | 1.86530 >= 0.892572 | True\n",
      "98) | For number: 505 | 2.09870 >= 1.135355 | True\n",
      "99) | For number: 817 | 2.16813 >= 1.209802 | True\n",
      "100) | For number: 685 | 2.14546 >= 1.183171 | True\n",
      "101) | For number: 541 | 2.10634 >= 1.146357 | True\n",
      "102) | For number: 262 | 1.98753 >= 1.023951 | True\n",
      "103) | For number: 603 | 2.12371 >= 1.163450 | True\n",
      "104) | For number: 933 | 2.18773 >= 1.229407 | True\n",
      "105) | For number: 562 | 2.10997 >= 1.152390 | True\n",
      "106) | For number: 303 | 2.01286 >= 1.049725 | True\n",
      "107) | For number: 819 | 2.16813 >= 1.210166 | True\n",
      "108) | For number: 469 | 2.08853 >= 1.123403 | True\n",
      "109) | For number: 398 | 2.05878 >= 1.096352 | True\n",
      "110) | For number: 887 | 2.18336 >= 1.221986 | True\n",
      "111) | For number: 774 | 2.16313 >= 1.201706 | True\n",
      "112) | For number: 848 | 2.17417 >= 1.215340 | True\n",
      "113) | For number: 739 | 2.15522 >= 1.194725 | True\n",
      "114) | For number: 797 | 2.16566 >= 1.206099 | True\n",
      "115) | For number: 134 | 1.86530 >= 0.895647 | True\n",
      "116) | For number: 523 | 2.10449 >= 1.140966 | True\n",
      "117) | For number: 869 | 2.17883 >= 1.218961 | True\n",
      "118) | For number: 740 | 2.15522 >= 1.194930 | True\n",
      "119) | For number: 151 | 1.89313 >= 0.919741 | True\n",
      "120) | For number: 301 | 2.01286 >= 1.048566 | True\n",
      "121) | For number: 477 | 2.08853 >= 1.126149 | True\n",
      "122) | For number: 711 | 2.14974 >= 1.188860 | True\n",
      "123) | For number: 332 | 2.02870 >= 1.065596 | True\n",
      "124) | For number: 240 | 1.97551 >= 1.008075 | True\n",
      "125) | For number: 207 | 1.94903 >= 0.980714 | True\n",
      "126) | For number: 647 | 2.13647 >= 1.174392 | True\n",
      "127) | For number: 728 | 2.15251 >= 1.192452 | True\n",
      "128) | For number: 508 | 2.09870 >= 1.136306 | True\n",
      "129) | For number: 906 | 2.18336 >= 1.225104 | True\n",
      "130) | For number: 900 | 2.18336 >= 1.224128 | True\n",
      "131) | For number: 868 | 2.17883 >= 1.218791 | True\n",
      "132) | For number: 139 | 1.87980 >= 0.903099 | True\n",
      "133) | For number: 384 | 2.05369 >= 1.090352 | True\n",
      "134) | For number: 770 | 2.16184 >= 1.200927 | True\n",
      "135) | For number: 480 | 2.09062 >= 1.127165 | True\n",
      "136) | For number: 118 | 1.84980 >= 0.869343 | True\n",
      "137) | For number: 230 | 1.96703 >= 1.000279 | True\n",
      "138) | For number: 742 | 2.15522 >= 1.195338 | True\n",
      "139) | For number: 298 | 2.01286 >= 1.046809 | True\n",
      "140) | For number: 299 | 2.01286 >= 1.047397 | True\n",
      "141) | For number: 692 | 2.14690 >= 1.184727 | True\n",
      "142) | For number: 780 | 2.16313 >= 1.202866 | True\n",
      "143) | For number: 625 | 2.13022 >= 1.169032 | True\n",
      "144) | For number: 403 | 2.06127 >= 1.098435 | True\n",
      "145) | For number: 546 | 2.10634 >= 1.147818 | True\n",
      "146) | For number: 102 | 1.81272 >= 0.838323 | True\n",
      "147) | For number: 614 | 2.12699 >= 1.166270 | True\n",
      "148) | For number: 183 | 1.92852 >= 0.957334 | True\n",
      "149) | For number: 992 | 2.19708 >= 1.238334 | True\n",
      "150) | For number: 453 | 2.07987 >= 1.117743 | True\n",
      "151) | For number: 928 | 2.18665 >= 1.228621 | True\n",
      "152) | For number: 750 | 2.15657 >= 1.196959 | True\n",
      "153) | For number: 883 | 2.18224 >= 1.221320 | True\n",
      "154) | For number: 920 | 2.18665 >= 1.227353 | True\n",
      "155) | For number: 206 | 1.94903 >= 0.979806 | True\n",
      "156) | For number: 920 | 2.18665 >= 1.227353 | True\n",
      "157) | For number: 432 | 2.07080 >= 1.109952 | True\n",
      "158) | For number: 985 | 2.19607 >= 1.237307 | True\n",
      "159) | For number: 172 | 1.91162 >= 0.945363 | True\n",
      "160) | For number: 282 | 2.00591 >= 1.037075 | True\n",
      "161) | For number: 467 | 2.08853 >= 1.122708 | True\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "162) | For number: 823 | 2.17056 >= 1.210892 | True\n",
      "163) | For number: 727 | 2.15251 >= 1.192243 | True\n",
      "164) | For number: 660 | 2.13952 >= 1.177460 | True\n",
      "165) | For number: 414 | 2.06372 >= 1.102914 | True\n",
      "166) | For number: 452 | 2.07987 >= 1.117382 | True\n",
      "167) | For number: 669 | 2.14103 >= 1.179544 | True\n",
      "168) | For number: 222 | 1.95377 >= 0.993747 | True\n",
      "169) | For number: 190 | 1.92852 >= 0.964514 | True\n",
      "170) | For number: 241 | 1.97966 >= 1.008833 | True\n",
      "171) | For number: 265 | 1.99133 >= 1.025993 | True\n",
      "172) | For number: 663 | 2.14103 >= 1.178159 | True\n",
      "173) | For number: 135 | 1.86530 >= 0.897164 | True\n",
      "174) | For number: 503 | 2.09870 >= 1.134718 | True\n",
      "175) | For number: 761 | 2.16054 >= 1.199156 | True\n",
      "176) | For number: 540 | 2.10449 >= 1.146063 | True\n",
      "177) | For number: 758 | 2.15922 >= 1.198561 | True\n",
      "178) | For number: 845 | 2.17417 >= 1.214814 | True\n",
      "179) | For number: 136 | 1.86530 >= 0.898667 | True\n",
      "180) | For number: 604 | 2.12371 >= 1.163709 | True\n",
      "181) | For number: 540 | 2.10449 >= 1.146063 | True\n",
      "182) | For number: 653 | 2.13800 >= 1.175817 | True\n",
      "183) | For number: 865 | 2.17883 >= 1.218279 | True\n",
      "184) | For number: 114 | 1.84980 >= 0.862088 | True\n",
      "185) | For number: 173 | 1.91740 >= 0.946488 | True\n",
      "186) | For number: 200 | 1.94903 >= 0.974242 | True\n",
      "187) | For number: 103 | 1.82243 >= 0.840431 | True\n",
      "188) | For number: 422 | 2.06848 >= 1.106085 | True\n",
      "189) | For number: 785 | 2.16313 >= 1.203825 | True\n",
      "190) | For number: 641 | 2.13337 >= 1.172951 | True\n",
      "191) | For number: 809 | 2.16689 >= 1.208333 | True\n",
      "192) | For number: 631 | 2.13181 >= 1.170515 | True\n",
      "193) | For number: 318 | 2.02568 >= 1.058146 | True\n",
      "194) | For number: 521 | 2.10258 >= 1.140354 | True\n",
      "195) | For number: 103 | 1.82243 >= 0.840431 | True\n",
      "196) | For number: 282 | 2.00591 >= 1.037075 | True\n",
      "197) | For number: 439 | 2.07538 >= 1.112597 | True\n",
      "198) | For number: 637 | 2.13181 >= 1.171982 | True\n",
      "199) | For number: 118 | 1.84980 >= 0.869343 | True\n",
      "200) | For number: 373 | 2.04844 >= 1.085456 | True\n",
      "201) | For number: 278 | 2.00235 >= 1.034540 | True\n",
      "202) | For number: 276 | 1.99874 >= 1.033256 | True\n",
      "203) | For number: 179 | 1.92299 >= 0.953083 | True\n",
      "204) | For number: 157 | 1.89950 >= 0.927477 | True\n",
      "205) | For number: 530 | 2.10449 >= 1.143088 | True\n",
      "206) | For number: 875 | 2.17883 >= 1.219978 | True\n",
      "207) | For number: 110 | 1.84095 >= 0.854518 | True\n",
      "208) | For number: 273 | 1.99874 >= 1.031309 | True\n",
      "209) | For number: 184 | 1.92852 >= 0.958380 | True\n",
      "210) | For number: 285 | 2.00944 >= 1.038949 | True\n",
      "211) | For number: 782 | 2.16313 >= 1.203251 | True\n",
      "212) | For number: 624 | 2.13022 >= 1.168783 | True\n",
      "213) | For number: 307 | 2.01611 >= 1.052018 | True\n",
      "214) | For number: 106 | 1.82243 >= 0.846606 | True\n",
      "215) | For number: 392 | 2.05626 >= 1.093811 | True\n",
      "216) | For number: 573 | 2.11525 >= 1.155447 | True\n",
      "217) | For number: 433 | 2.07311 >= 1.110333 | True\n",
      "218) | For number: 395 | 2.05626 >= 1.095087 | True\n",
      "219) | For number: 323 | 2.02568 >= 1.060850 | True\n",
      "220) | For number: 721 | 2.15113 >= 1.190985 | True\n",
      "221) | For number: 117 | 1.84980 >= 0.867557 | True\n",
      "222) | For number: 621 | 2.13022 >= 1.168034 | True\n",
      "223) | For number: 775 | 2.16313 >= 1.201900 | True\n",
      "224) | For number: 596 | 2.12037 >= 1.161625 | True\n",
      "225) | For number: 721 | 2.15113 >= 1.190985 | True\n",
      "226) | For number: 494 | 2.09471 >= 1.131811 | True\n",
      "227) | For number: 347 | 2.03455 >= 1.073179 | True\n",
      "228) | For number: 426 | 2.06848 >= 1.107645 | True\n",
      "229) | For number: 336 | 2.02870 >= 1.067657 | True\n",
      "230) | For number: 774 | 2.16313 >= 1.201706 | True\n",
      "231) | For number: 409 | 2.06372 >= 1.100896 | True\n",
      "232) | For number: 531 | 2.10449 >= 1.143388 | True\n",
      "233) | For number: 247 | 1.97966 >= 1.013306 | True\n",
      "234) | For number: 757 | 2.15922 >= 1.198362 | True\n",
      "235) | For number: 228 | 1.96266 >= 0.998671 | True\n",
      "236) | For number: 290 | 2.00944 >= 1.042021 | True\n",
      "237) | For number: 612 | 2.12535 >= 1.165762 | True\n",
      "238) | For number: 496 | 2.09471 >= 1.132462 | True\n",
      "239) | For number: 897 | 2.18336 >= 1.223637 | True\n",
      "240) | For number: 748 | 2.15657 >= 1.196556 | True\n",
      "241) | For number: 946 | 2.18986 >= 1.231429 | True\n",
      "242) | For number: 357 | 2.04025 >= 1.078024 | True\n",
      "243) | For number: 476 | 2.08853 >= 1.125809 | True\n",
      "244) | For number: 718 | 2.14974 >= 1.190351 | True\n",
      "245) | For number: 628 | 2.13022 >= 1.169776 | True\n",
      "246) | For number: 265 | 1.99133 >= 1.025993 | True\n",
      "247) | For number: 151 | 1.89313 >= 0.919741 | True\n",
      "248) | For number: 878 | 2.17997 >= 1.220483 | True\n",
      "249) | For number: 383 | 2.05369 >= 1.089914 | True\n",
      "250) | For number: 594 | 2.12037 >= 1.161099 | True\n",
      "251) | For number: 309 | 2.01611 >= 1.053151 | True\n",
      "252) | For number: 570 | 2.11350 >= 1.154620 | True\n",
      "253) | For number: 772 | 2.16184 >= 1.201317 | True\n",
      "254) | For number: 655 | 2.13800 >= 1.176288 | True\n",
      "255) | For number: 789 | 2.16440 >= 1.204588 | True\n",
      "256) | For number: 646 | 2.13492 >= 1.174152 | True\n",
      "257) | For number: 636 | 2.13181 >= 1.171739 | True\n",
      "258) | For number: 126 | 1.84980 >= 0.882999 | True\n",
      "259) | For number: 338 | 2.03167 >= 1.068676 | True\n",
      "260) | For number: 975 | 2.19403 >= 1.235826 | True\n",
      "261) | For number: 570 | 2.11350 >= 1.154620 | True\n",
      "262) | For number: 280 | 2.00235 >= 1.035813 | True\n",
      "263) | For number: 416 | 2.06372 >= 1.103713 | True\n",
      "264) | For number: 923 | 2.18665 >= 1.227830 | True\n",
      "265) | For number: 164 | 1.90564 >= 0.936067 | True\n",
      "266) | For number: 475 | 2.08853 >= 1.125468 | True\n",
      "267) | For number: 479 | 2.09062 >= 1.126827 | True\n",
      "268) | For number: 738 | 2.15387 >= 1.194520 | True\n",
      "269) | For number: 115 | 1.84980 >= 0.863930 | True\n",
      "270) | For number: 182 | 1.92852 >= 0.956282 | True\n",
      "271) | For number: 338 | 2.03167 >= 1.068676 | True\n",
      "272) | For number: 545 | 2.10634 >= 1.147527 | True\n",
      "273) | For number: 624 | 2.13022 >= 1.168783 | True\n",
      "274) | For number: 694 | 2.14690 >= 1.185168 | True\n",
      "275) | For number: 956 | 2.19196 >= 1.232962 | True\n",
      "276) | For number: 797 | 2.16566 >= 1.206099 | True\n",
      "277) | For number: 907 | 2.18447 >= 1.225266 | True\n",
      "278) | For number: 778 | 2.16313 >= 1.202481 | True\n",
      "279) | For number: 722 | 2.15113 >= 1.191195 | True\n",
      "280) | For number: 913 | 2.18556 >= 1.226234 | True\n",
      "281) | For number: 541 | 2.10634 >= 1.146357 | True\n",
      "282) | For number: 328 | 2.02568 >= 1.063505 | True\n",
      "283) | For number: 245 | 1.97966 >= 1.011830 | True\n",
      "284) | For number: 757 | 2.15922 >= 1.198362 | True\n",
      "285) | For number: 270 | 1.99505 >= 1.029338 | True\n",
      "286) | For number: 215 | 1.95377 >= 0.987800 | True\n",
      "287) | For number: 110 | 1.84095 >= 0.854518 | True\n",
      "288) | For number: 361 | 2.04303 >= 1.079918 | True\n",
      "289) | For number: 213 | 1.95377 >= 0.986058 | True\n",
      "290) | For number: 101 | 1.81272 >= 0.836191 | True\n",
      "291) | For number: 613 | 2.12699 >= 1.166016 | True\n",
      "292) | For number: 825 | 2.17056 >= 1.211254 | True\n",
      "293) | For number: 562 | 2.10997 >= 1.152390 | True\n",
      "294) | For number: 960 | 2.19196 >= 1.233570 | True\n",
      "295) | For number: 965 | 2.19196 >= 1.234327 | True\n",
      "296) | For number: 694 | 2.14690 >= 1.185168 | True\n",
      "297) | For number: 406 | 2.06127 >= 1.099671 | True\n",
      "298) | For number: 720 | 2.15113 >= 1.190774 | True\n",
      "299) | For number: 963 | 2.19196 >= 1.234025 | True\n",
      "300) | For number: 331 | 2.02870 >= 1.065076 | True\n",
      "301) | For number: 240 | 1.97551 >= 1.008075 | True\n",
      "302) | For number: 604 | 2.12371 >= 1.163709 | True\n",
      "303) | For number: 954 | 2.19196 >= 1.232657 | True\n",
      "304) | For number: 218 | 1.95377 >= 0.990376 | True\n",
      "305) | For number: 678 | 2.14399 >= 1.181596 | True\n",
      "306) | For number: 999 | 2.19808 >= 1.239353 | True\n",
      "307) | For number: 348 | 2.03455 >= 1.073671 | True\n",
      "308) | For number: 298 | 2.01286 >= 1.046809 | True\n",
      "309) | For number: 685 | 2.14546 >= 1.183171 | True\n",
      "310) | For number: 543 | 2.10634 >= 1.146944 | True\n",
      "311) | For number: 760 | 2.15922 >= 1.198958 | True\n",
      "312) | For number: 874 | 2.17883 >= 1.219809 | True\n",
      "313) | For number: 541 | 2.10634 >= 1.146357 | True\n",
      "314) | For number: 467 | 2.08853 >= 1.122708 | True\n",
      "315) | For number: 788 | 2.16440 >= 1.204397 | True\n",
      "316) | For number: 354 | 2.04025 >= 1.076588 | True\n",
      "317) | For number: 692 | 2.14690 >= 1.184727 | True\n",
      "318) | For number: 121 | 1.84980 >= 0.874591 | True\n",
      "319) | For number: 776 | 2.16313 >= 1.202094 | True\n",
      "320) | For number: 730 | 2.15251 >= 1.192868 | True\n",
      "321) | For number: 360 | 2.04303 >= 1.079447 | True\n",
      "322) | For number: 751 | 2.15790 >= 1.197161 | True\n",
      "323) | For number: 401 | 2.06127 >= 1.097605 | True\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "324) | For number: 809 | 2.16689 >= 1.208333 | True\n",
      "325) | For number: 560 | 2.10997 >= 1.151827 | True\n",
      "326) | For number: 103 | 1.82243 >= 0.840431 | True\n",
      "327) | For number: 591 | 2.11869 >= 1.160306 | True\n",
      "328) | For number: 167 | 1.91162 >= 0.939615 | True\n",
      "329) | For number: 791 | 2.16440 >= 1.204967 | True\n",
      "330) | For number: 926 | 2.18665 >= 1.228305 | True\n",
      "331) | For number: 913 | 2.18556 >= 1.226234 | True\n",
      "332) | For number: 355 | 2.04025 >= 1.077068 | True\n",
      "333) | For number: 482 | 2.09062 >= 1.127838 | True\n",
      "334) | For number: 404 | 2.06127 >= 1.098848 | True\n",
      "335) | For number: 851 | 2.17417 >= 1.215864 | True\n",
      "336) | For number: 745 | 2.15657 >= 1.195948 | True\n",
      "337) | For number: 805 | 2.16566 >= 1.207593 | True\n",
      "338) | For number: 156 | 1.89313 >= 0.926213 | True\n",
      "339) | For number: 254 | 1.98364 >= 1.018366 | True\n",
      "340) | For number: 920 | 2.18665 >= 1.227353 | True\n",
      "341) | For number: 661 | 2.14103 >= 1.177694 | True\n",
      "342) | For number: 316 | 2.02252 >= 1.057051 | True\n",
      "343) | For number: 814 | 2.16813 >= 1.209253 | True\n",
      "344) | For number: 612 | 2.12535 >= 1.165762 | True\n",
      "345) | For number: 988 | 2.19607 >= 1.237748 | True\n",
      "346) | For number: 803 | 2.16566 >= 1.207221 | True\n",
      "347) | For number: 370 | 2.04576 >= 1.084091 | True\n",
      "348) | For number: 538 | 2.10449 >= 1.145473 | True\n",
      "349) | For number: 805 | 2.16566 >= 1.207593 | True\n",
      "350) | For number: 941 | 2.18986 >= 1.230655 | True\n",
      "351) | For number: 769 | 2.16184 >= 1.200731 | True\n",
      "352) | For number: 588 | 2.11869 >= 1.159508 | True\n",
      "353) | For number: 657 | 2.13800 >= 1.176758 | True\n",
      "354) | For number: 789 | 2.16440 >= 1.204588 | True\n",
      "355) | For number: 856 | 2.17534 >= 1.216732 | True\n",
      "356) | For number: 979 | 2.19505 >= 1.236420 | True\n",
      "357) | For number: 434 | 2.07311 >= 1.110713 | True\n",
      "358) | For number: 555 | 2.10817 >= 1.150409 | True\n",
      "359) | For number: 731 | 2.15251 >= 1.193076 | True\n",
      "360) | For number: 987 | 2.19607 >= 1.237601 | True\n",
      "361) | For number: 231 | 1.96703 >= 1.001076 | True\n",
      "362) | For number: 972 | 2.19403 >= 1.235378 | True\n",
      "363) | For number: 572 | 2.11525 >= 1.155172 | True\n",
      "364) | For number: 986 | 2.19607 >= 1.237454 | True\n",
      "365) | For number: 657 | 2.13800 >= 1.176758 | True\n",
      "366) | For number: 695 | 2.14690 >= 1.185388 | True\n",
      "367) | For number: 248 | 1.97966 >= 1.014040 | True\n",
      "368) | For number: 862 | 2.17767 >= 1.217766 | True\n",
      "369) | For number: 477 | 2.08853 >= 1.126149 | True\n",
      "370) | For number: 923 | 2.18665 >= 1.227830 | True\n",
      "371) | For number: 426 | 2.06848 >= 1.107645 | True\n",
      "372) | For number: 702 | 2.14833 >= 1.186918 | True\n",
      "373) | For number: 997 | 2.19808 >= 1.239063 | True\n",
      "374) | For number: 194 | 1.93893 >= 0.968477 | True\n",
      "375) | For number: 200 | 1.94903 >= 0.974242 | True\n",
      "376) | For number: 357 | 2.04025 >= 1.078024 | True\n",
      "377) | For number: 466 | 2.08639 >= 1.122359 | True\n",
      "378) | For number: 306 | 2.01286 >= 1.051448 | True\n",
      "379) | For number: 640 | 2.13181 >= 1.172709 | True\n",
      "380) | For number: 967 | 2.19300 >= 1.234628 | True\n",
      "381) | For number: 316 | 2.02252 >= 1.057051 | True\n",
      "382) | For number: 655 | 2.13800 >= 1.176288 | True\n",
      "383) | For number: 101 | 1.81272 >= 0.836191 | True\n",
      "384) | For number: 836 | 2.17297 >= 1.213224 | True\n",
      "385) | For number: 980 | 2.19505 >= 1.236569 | True\n",
      "386) | For number: 642 | 2.13337 >= 1.173192 | True\n",
      "387) | For number: 130 | 1.85767 >= 0.889440 | True\n",
      "388) | For number: 965 | 2.19196 >= 1.234327 | True\n",
      "389) | For number: 860 | 2.17767 >= 1.217422 | True\n",
      "390) | For number: 583 | 2.11698 >= 1.158168 | True\n",
      "391) | For number: 606 | 2.12371 >= 1.164225 | True\n",
      "392) | For number: 405 | 2.06127 >= 1.099260 | True\n",
      "393) | For number: 517 | 2.10066 >= 1.139121 | True\n",
      "394) | For number: 410 | 2.06372 >= 1.101302 | True\n",
      "395) | For number: 793 | 2.16440 >= 1.205345 | True\n",
      "396) | For number: 679 | 2.14399 >= 1.181822 | True\n",
      "397) | For number: 786 | 2.16313 >= 1.204016 | True\n",
      "398) | For number: 308 | 2.01611 >= 1.052586 | True\n",
      "399) | For number: 501 | 2.09671 >= 1.134077 | True\n",
      "400) | For number: 507 | 2.09870 >= 1.135990 | True\n",
      "401) | For number: 946 | 2.18986 >= 1.231429 | True\n",
      "402) | For number: 181 | 1.92852 >= 0.955222 | True\n",
      "403) | For number: 730 | 2.15251 >= 1.192868 | True\n",
      "404) | For number: 186 | 1.92852 >= 0.960451 | True\n",
      "405) | For number: 214 | 1.95377 >= 0.986931 | True\n",
      "406) | For number: 411 | 2.06372 >= 1.101706 | True\n",
      "407) | For number: 258 | 1.98753 >= 1.021184 | True\n",
      "408) | For number: 678 | 2.14399 >= 1.181596 | True\n",
      "409) | For number: 249 | 1.97966 >= 1.014769 | True\n",
      "410) | For number: 209 | 1.94903 >= 0.982516 | True\n",
      "411) | For number: 535 | 2.10449 >= 1.144584 | True\n",
      "412) | For number: 857 | 2.17651 >= 1.216905 | True\n",
      "413) | For number: 892 | 2.18336 >= 1.222814 | True\n",
      "414) | For number: 491 | 2.09471 >= 1.130828 | True\n",
      "415) | For number: 587 | 2.11869 >= 1.159241 | True\n",
      "416) | For number: 989 | 2.19607 >= 1.237895 | True\n",
      "417) | For number: 977 | 2.19505 >= 1.236123 | True\n",
      "418) | For number: 163 | 1.90564 >= 0.934867 | True\n",
      "419) | For number: 191 | 1.93375 >= 0.965514 | True\n",
      "420) | For number: 822 | 2.16934 >= 1.210711 | True\n",
      "421) | For number: 222 | 1.95377 >= 0.993747 | True\n",
      "422) | For number: 1000 | 2.19808 >= 1.239498 | True\n",
      "423) | For number: 484 | 2.09062 >= 1.128508 | True\n",
      "424) | For number: 636 | 2.13181 >= 1.171739 | True\n",
      "425) | For number: 985 | 2.19607 >= 1.237307 | True\n",
      "426) | For number: 223 | 1.95826 >= 0.994579 | True\n",
      "427) | For number: 548 | 2.10817 >= 1.148398 | True\n",
      "428) | For number: 351 | 2.03741 >= 1.075137 | True\n",
      "429) | For number: 474 | 2.08853 >= 1.125126 | True\n",
      "430) | For number: 598 | 2.12037 >= 1.162149 | True\n",
      "431) | For number: 720 | 2.15113 >= 1.190774 | True\n",
      "432) | For number: 577 | 2.11698 >= 1.156542 | True\n",
      "433) | For number: 340 | 2.03167 >= 1.069689 | True\n",
      "434) | For number: 364 | 2.04303 >= 1.081323 | True\n",
      "435) | For number: 671 | 2.14103 >= 1.180003 | True\n",
      "436) | For number: 971 | 2.19403 >= 1.235228 | True\n",
      "437) | For number: 220 | 1.95377 >= 0.992071 | True\n",
      "438) | For number: 581 | 2.11698 >= 1.157628 | True\n",
      "439) | For number: 112 | 1.84095 >= 0.858344 | True\n",
      "440) | For number: 544 | 2.10634 >= 1.147236 | True\n",
      "441) | For number: 348 | 2.03455 >= 1.073671 | True\n",
      "442) | For number: 391 | 2.05626 >= 1.093383 | True\n",
      "443) | For number: 798 | 2.16566 >= 1.206286 | True\n",
      "444) | For number: 260 | 1.98753 >= 1.022574 | True\n",
      "445) | For number: 222 | 1.95377 >= 0.993747 | True\n",
      "446) | For number: 759 | 2.15922 >= 1.198760 | True\n",
      "447) | For number: 445 | 2.07764 >= 1.114826 | True\n",
      "448) | For number: 769 | 2.16184 >= 1.200731 | True\n",
      "449) | For number: 252 | 1.98364 >= 1.016937 | True\n",
      "450) | For number: 992 | 2.19708 >= 1.238334 | True\n",
      "451) | For number: 654 | 2.13800 >= 1.176053 | True\n",
      "452) | For number: 202 | 1.94903 >= 0.976118 | True\n",
      "453) | For number: 718 | 2.14974 >= 1.190351 | True\n",
      "454) | For number: 734 | 2.15387 >= 1.193697 | True\n",
      "455) | For number: 983 | 2.19607 >= 1.237012 | True\n",
      "456) | For number: 677 | 2.14399 >= 1.181370 | True\n",
      "457) | For number: 821 | 2.16934 >= 1.210530 | True\n",
      "458) | For number: 324 | 2.02568 >= 1.061385 | True\n",
      "459) | For number: 125 | 1.84980 >= 0.881350 | True\n",
      "460) | For number: 895 | 2.18336 >= 1.223308 | True\n",
      "461) | For number: 813 | 2.16813 >= 1.209069 | True\n",
      "462) | For number: 787 | 2.16440 >= 1.204207 | True\n",
      "463) | For number: 834 | 2.17297 >= 1.212868 | True\n",
      "464) | For number: 226 | 1.95826 >= 0.997047 | True\n",
      "465) | For number: 734 | 2.15387 >= 1.193697 | True\n",
      "466) | For number: 599 | 2.12204 >= 1.162410 | True\n",
      "467) | For number: 136 | 1.86530 >= 0.898667 | True\n",
      "468) | For number: 477 | 2.08853 >= 1.126149 | True\n",
      "469) | For number: 313 | 2.02252 >= 1.055392 | True\n",
      "470) | For number: 212 | 1.95377 >= 0.985180 | True\n",
      "471) | For number: 693 | 2.14690 >= 1.184947 | True\n",
      "472) | For number: 864 | 2.17883 >= 1.218108 | True\n",
      "473) | For number: 136 | 1.86530 >= 0.898667 | True\n",
      "474) | For number: 998 | 2.19808 >= 1.239208 | True\n",
      "475) | For number: 933 | 2.18773 >= 1.229407 | True\n",
      "476) | For number: 676 | 2.14252 >= 1.181143 | True\n",
      "477) | For number: 315 | 2.02252 >= 1.056500 | True\n",
      "478) | For number: 365 | 2.04303 >= 1.081788 | True\n",
      "479) | For number: 792 | 2.16440 >= 1.205156 | True\n",
      "480) | For number: 180 | 1.92299 >= 0.954156 | True\n",
      "481) | For number: 671 | 2.14103 >= 1.180003 | True\n",
      "482) | For number: 349 | 2.03741 >= 1.074161 | True\n",
      "483) | For number: 921 | 2.18665 >= 1.227513 | True\n",
      "484) | For number: 566 | 2.11174 >= 1.153510 | True\n",
      "485) | For number: 797 | 2.16566 >= 1.206099 | True\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "486) | For number: 480 | 2.09062 >= 1.127165 | True\n",
      "487) | For number: 604 | 2.12371 >= 1.163709 | True\n",
      "488) | For number: 305 | 2.01286 >= 1.050876 | True\n",
      "489) | For number: 466 | 2.08639 >= 1.122359 | True\n",
      "490) | For number: 465 | 2.08639 >= 1.122009 | True\n",
      "491) | For number: 858 | 2.17651 >= 1.217077 | True\n",
      "492) | For number: 311 | 2.01933 >= 1.054276 | True\n",
      "493) | For number: 894 | 2.18336 >= 1.223144 | True\n",
      "494) | For number: 916 | 2.18556 >= 1.226715 | True\n",
      "495) | For number: 255 | 1.98364 >= 1.019075 | True\n",
      "496) | For number: 374 | 2.04844 >= 1.085908 | True\n",
      "497) | For number: 821 | 2.16934 >= 1.210530 | True\n",
      "498) | For number: 950 | 2.19091 >= 1.232044 | True\n",
      "499) | For number: 832 | 2.17297 >= 1.212511 | True\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "from numpy import log as ln\n",
    "n = 500            # Number of times i will test the formula\n",
    "smallest = 100    # Smallest value that can be tested\n",
    "biggest = 1000   # Biggest value that can be tested\n",
    "\n",
    "# First 2 functions are modified code snippets from https://code.sololearn.com/ckLyQdziTJHc/#py\n",
    "from numpy import log as ln\n",
    "from mpmath import li\n",
    "\n",
    "def f(x):\n",
    "    if x == 0:\n",
    "        return 1 \n",
    "    else:\n",
    "        total = 1\n",
    "        while(x>0):\n",
    "            total *= x\n",
    "            x -= 1\n",
    "        return total \n",
    "\n",
    "# Here we will use the wilsons theorem for prime numbers, stating that a natural number n > 1 is a prime number \n",
    "# if and only if the product of all the positive integers less than n is one less than a multiple of n.\n",
    "\n",
    "def wilson(x):\n",
    "    if(f(x-1)%x==(x-1) and x!=1):\n",
    "        return 1\n",
    "    else:\n",
    "        return 0 \n",
    "\n",
    "# Here i compute π(x), but the result is the sum 1/p for all the primes < x, not the number of primes as in regular π(x)\n",
    "    \n",
    "def π_primeSum(x):\n",
    "    summ=0\n",
    "    for i in range(1,x+1):\n",
    "        if(wilson(i)==1):\n",
    "            summ=summ+1/i\n",
    "    return summ\n",
    "\n",
    "\n",
    "print(\"No |The Chosen Number| Σ(1/p) >= lnlnx-ln2 | Validation\")\n",
    "print(\"--------------------------------------------------------\")\n",
    "for i in range(n):\n",
    "    summ=0 \n",
    "    validation = True\n",
    "    x = random.randint(smallest,biggest)      # Pick a large number each time\n",
    "    lnexpr = ln(ln(x)) - ln(2)                # Compute the right expression \n",
    "    Σexpr = π_primeSum(x)\n",
    "    valid = Σexpr>=lnexpr\n",
    "    if (valid==False):                        # If even one is false, formula is invalid\n",
    "        validation = False\n",
    "        print(\"Formula is invalid\")\n",
    "        break\n",
    "    \n",
    "#     for j in range (1,x):\n",
    "#         summ = summ + 1/j                     # Compute the left expression\n",
    "#         valid = summ>=lnexpr\n",
    "#     if (valid==False):                        # If even one is false, formula is invalid\n",
    "#         validation = False\n",
    "#         print(\"Formula is invalid\")\n",
    "#         break\n",
    "\n",
    "    print(str(i) + \") | For number: \" + str(x) + \" | \" + str(\"%.5f\" % Σexpr) + \" >= \" + str(\"%.6f\" % lnexpr) + \" | \" + str(valid))\n",
    "        "
   ]
  }
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