Finds prime numbers that are also limericks. Inspired by the post Limerick primes by John D. Cook, although he's looking for a smaller, simpler pattern, like 11551. This code looks for a prime number that, when read aloud, works like a limerick. For example:
23444683
93324223
96296
98326
46359543
The pattern of syllables looks like this, with * being the emphasized ones.
1*11*11*
1*11*11*
1*11*
1*11*
1*11*11*
Constraints:
- Digits with one syllable: one, two, three, four, five, six, eight, nine.
- Digits with two syllables: zero, seven.
- The zero and seven replace two digits and can only appear in position 2 (any line) or 5 (lines 1, 2, or 5).
- Lines 1, 2, and 5 must rhyme.
- Lines 3 and 4 must rhyme.
- None of the digits rhyme with each other, so can only rhyme with themselves.
We can simplify by skipping zero and seven so that we have a consistent number of digits. The pattern for the last digit is:
1*11*11x
1*11*11x
1*11y
1*11y
1*11*11x
- x can't be 0, 2, 4, 6, 8, or 5 (not prime) or 7 (two syllables). Must be one of: 1, 3, 9.
- y can't be 0 or 7 (two syllables). Must be one of: 1, 2, 3, 4, 5, 6, 8, 9.
- That's 3×8 = 24 possibilities.
- If using only one-syllable digits, there are 7×3 + 4×2 = 29 remaining digits, each can be 8 values, so that's 8^29 possibilities.
- Altogether there are 8×3 + 5×2 = 34 digits in the number.
The LimerickPrime.java program generates a random 34-digit number and then
tries all the values for x and y. Run with:
% ./GO
Copyright 2015 Lawrence Kesteloot
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
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