

A165235


Least prime p such that the n+1 numbers p + 2^k  2, k=1..n+1, are all prime.


0




OFFSET

1,1


COMMENTS

The n+1 primes have common differences of 2^k for k=1..n. For any n, the set {2^k  2, k=1..n+1} is admissible. Hence by the prime ktuple conjecture, an infinite number of primes p should exist for each n. Note that a(1) is the first term of the twin primes A001359 and a(2) is the first term of prime triples A022004. The a(12) term is greater than 10^12.


LINKS



EXAMPLE

a(5)=17 because {17,19,23,31,47,79} are 6 primes whose differences are powers of 2, and 17 is the least such prime.


MATHEMATICA

p=3; Table[While[ !And@@PrimeQ[p+2^Range[2, n+1]2], p=NextPrime[p]]; p, {n, 8}]


CROSSREFS



KEYWORD

hard,nonn


AUTHOR



STATUS

approved



