[seqfan] Re: Christmas puzzle: What is the next number in the sequence 2, 3, ...?

[Robert Israel]

If p == 1 mod 3, 2p+1 == 0 mod 3.  If p == 2 mod 3, 2p-1 == 0 mod 3.
So there are no such p > 3.

Cheers,
Robert Israel


On Fri, 25 Dec 2009, mathstutoring wrote:

> Consider the sequence of integers p for which p is prime and 2p-1 and 2p+1 are a pair of twin primes.
>
> Does anyone know what the next term is (if it exists it is greater than 2.5 x 10^9), or have a proof that the above sequence is complete?
>
> One to ponder after the Christmas turkey
>
> Ant
>
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