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## Prime double pairs.

Starting at 10, for any set of 5 consecutive odd numbers, at most 4 can be prime (the number ending in 5 cannot be prime). Moreover any such set has to have the number ending in 5 as the middle of two pairs of prime (you cannot have 3 consecutive odd primes when you start after 10). The first example of such a set is 11, 13, 17, 19. The next is 101, 103, 107, 109. How frequently does such a sequence occur? Is it known if there are an infinite number of such pairs of pairs?
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 mostly related with the twin prime conjecture. If there exists an infinite of twin primes ( im quite sure there is ) then IT IS possible that there exist an infinite of such sequences. Still an open problem, il try to close it this summer.
 Recognitions: Homework Help Science Advisor Recent work has shown there exists an infinite number of arithmetic series within primes. Using your example of 11, 13, 17, 19. Is the same as 9 + 2n for n = 1, 2, 3, 4. Saying in this sequence that the number of terms is 4, t = 4, the proof shows that there exists in primes arithmetic series of the form a + dn for all t. t = 22 is the largest that has ever been calculated: 11,410,337,850,553 + 4,609,098,694,200n for n = 1, 2, 3 … 22 However, the twin prime conjecture may be close to being solved, read here: http://mathworld.wolfram.com/news/20...09/twinprimes/ Sorry but I have not heard of your problem before.

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