A213107 Primes p such that 2p^2-1, 3p^2-2, 4p^2-3, and 5p^2-4 are also prime.

17569, 43781, 70321, 229561, 251231, 426131, 426551, 453289, 635051, 727201, 729791, 741709, 944689, 981091, 1015309, 1078081, 1128761, 1228429, 1231229, 1282961, 1289149, 1302349, 1351099, 1723481, 1763159, 1823779, 2078339, 2260889, 2336519, 2357879

Offset: 1

Author

Zak Seidov, Jun 05 2012

Keywords

• nonn
• easy

Comments

Subsequence of A213079: a(1) = 17569 = A213079(10) =A213078(44)= A106483(389) = A000040(2019).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..740

Crossrefs

Cf. A000040, A106483, A213078, A213079.

Programs

Magma

[p: p in PrimesUpTo(2500000) | forall{i*p^2-i+1: i in [2..5] | IsPrime(i*p^2-i+1)}]; // Vincenzo Librandi, Apr 08 2013

Mathematica

Select[Prime[Range[200000]], PrimeQ[2 #^2 - 1] && PrimeQ[3 #^2 - 2] && PrimeQ[4 #^2 - 3] && PrimeQ[5 #^2 - 4] &] (* T. D. Noe, Jun 06 2012 *)