Problems & Puzzles: Puzzles

Puzzle 470. p+2=semiprime JM Bergot sent one more nice observation: I have been informed that for each prime between 3,139,136,237 and 3,139,136,549 there are 11 primes p such that every p+2 is a semiprime    Q. If so, can you find more than 11 consecutive primes with this property?

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Contributions came fromJ. K. Andersen &  Farideh Firoozbakht

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J. K. Andersen wrote:

Bergot's example is the smallest with 11 primes.
Below are record runs (longer than for any smaller primes).
Length: Primes
1: 2
2: 19, 23
4: 109 to 131
7: 467 to 509
8: 347591 to 347717
9: 4294471 to 4294649
10: 10818641 to 10818917
11: 3139136237 to 3139136549
12: 46243324157 to 46243324649
13: 328628315459 to 328628315777

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Farideh Firoozbakht wrote:

12: 46243324157 to 46243324649

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