Problems & Puzzles: Puzzles

Puzzle 692 Consecutive prime gaps biprimes JM Bergot sent the following nice puzzle. "Find consecutive prime gaps such that all of these gaps are biprimes". The record about this question is 22 gaps after the prime 348705174313 . See http://oeis.org/A220697 Q. Find a larger set than 22 gaps.

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Contributions came from Giovanni Resta & Emmanuel Vantieghem.

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Giovanni wrote:

I stopped my search at 6*10^14. I found the earliest runs of exactly 23, 24 and 25 semiprime gaps.

Between 15234953708851 and 15234953709377 there are the 23 gaps
2 * {5, 3, 3, 13, 2, 37, 3, 5, 7, 11, 19, 2, 13, 3, 5, 7, 5, 13, 17, 3, 67, 3, 17}.

Between 163229981102789 and 163229981103199 there are the 24 gaps
2 * {7, 3, 2, 7, 2, 13, 3, 3, 29, 13, 17, 7, 11, 7, 5, 7, 3, 2, 19, 17, 3, 19, 3, 3}

Between 87255058923913 and 87255058924391 there are the 25 gaps
2 * {3, 17, 3, 7, 3, 2, 13, 17, 7, 3, 23, 19, 5, 7, 5, 13, 2, 13, 23, 19, 5, 13, 2, 13, 2}

Note that the first run of 25 gaps occurs earlier than the one of 24 gaps.

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Emmanuel wrote:

My PC found no solution below 4*10^11.

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