Problem 54755. List odd twin composites

Twin primes, or prime numbers that differ by 2 (e.g., 17 and 19, 59 and 61, or 191 and 193), are the subject of several Cody problems: 248, 1096, 3016, and 52298. (See also Cody Problem 53740 for “almost twin primes”.)
This problem deals with twin composites. Because all even numbers are twin composites, let’s focus on odd twin composites, such as 25 and 27, 63 and 65, and 169 and 171.
Write a function that takes a number and produces a two-column matrix with the smaller number of the odd twin composite pair in the first column and the larger in the second column.
Optional exercises: (a) prove that the number of odd twin composites is infinite, (b) prove that the number of twin primes is infinite.
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72.73% Correct | 27.27% Incorrect
Last Solution submitted on Sep 30, 2025

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