A225057 - OEIS

A225057

Least prime p such that p*6^n +/- 1 are primes.

2, 2, 2, 2, 47, 3, 53, 677, 823, 227, 1907, 1103, 17, 163, 2693, 1213, 277, 2767, 887, 8353, 1013, 773, 6967, 1423, 2593, 9643, 157, 18013, 263, 2137, 2837, 107, 3467, 2137, 17, 2777, 1453, 2683, 7963, 3517, 2767, 53527, 8563, 227, 367, 27673, 30853, 5087, 7723, 14753, 41687, 137, 48647, 26357, 16747, 2797, 9887, 35933

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OFFSET

1,1

COMMENTS

a(1) >= A064215(n). First n's such that a(n) = A064215(n): 2, 3, 4, 6, 13, 27, 29, 32, 35, 40, 44, 45, 52, 60, 67, 71, 79, 86, 87, 97, 99.

According to Dickson's Conjecture a(n) exists for any n.

LINKS

Table of n, a(n) for n=1..58.

Chris Caldwell, Prime Glossary: Dickson's Conjecture

MATHEMATICA

Table[ n6=6^n; p = 2; While[ ! PrimeQ[q = p*n6 + 1 ] || ! PrimeQ[ q - 2 ], p = NextPrime[p] ]; p, {n, 100}]

CROSSREFS