A127435 Primes p such that (p-1)^2 + 1 is prime.

2, 3, 5, 7, 11, 17, 37, 41, 67, 127, 131, 151, 157, 181, 211, 241, 251, 257, 271, 281, 307, 397, 401, 421, 431, 467, 491, 557, 571, 577, 647, 691, 701, 751, 761, 827, 907, 911, 937, 947, 967, 1061, 1097, 1151, 1277, 1291, 1307, 1321, 1367, 1567, 1571, 1861

Offset: 1

Author

Lekraj Beedassy, Jan 14 2007

Keywords

• nonn

Comments

Consists of 3 and a subsequence of A045349.

These are the primes of the form A067720(k)+1. - Michel Marcus, Nov 21 2020

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2289

Crossrefs

For the associated primes, see A127436.

Cf. A045349, A067720.

Programs

Magma

[p: p in PrimesUpTo(2000) | IsPrime((p^2-2*p+2))]; // Vincenzo Librandi, Jul 20 2025

Mathematica

Select[Prime@Range[300], PrimeQ[(# - 1)^2 + 1] &] (* Ray Chandler, Jan 23 2007 *)

PARI

listp(nn) = {forprime(p=2, nn, if (isprime((p-1)^2 + 1), print1(p, ", ")););} \\ Michel Marcus, Jun 08 2016

Formula

a(n) = sqrt(A127436(n)-1) + 1.

Extensions

Corrected and extended by Ray Chandler, Jan 23 2007