A085832 Smallest prime p such that both (p-1)/2^(2n-1) and 2^(2n-1)*p+1 are primes.

5, 17, 1889, 21377, 183809, 83969, 40961, 79003649, 245235713, 5767169, 1004535809, 897581057, 41238396929, 13555990529, 2357400174593, 3438121320449, 12360915877889, 188188287041537, 286010462175233

Offset: 1

Author

Robert G. Wilson v, Jul 26 2003

Keywords

• nonn

Comments

I have found no primes less than the 10^7th prime where an even power of 2 results in the two prime forms above simultaneously except for 2^2 and p=13.

Crossrefs

Cf. A059455, A085958, A086476, A086477, A086478.

Programs

Mathematica

f[n_] := Block[{k = 1}, While[ !PrimeQ[k] || !PrimeQ[(k - 1)/2^n] || !PrimeQ[2^n*k + 1], k += 2^n]; k]; Table[ f[n], {n, 1, 37, 2}]