A338570 Primes p such that q*r mod p is prime, where q is the prime preceding p and r is the prime following p.

11, 13, 19, 29, 31, 37, 47, 53, 59, 67, 73, 83, 89, 109, 127, 131, 151, 163, 173, 179, 211, 239, 251, 263, 269, 283, 307, 337, 359, 373, 383, 421, 433, 443, 449, 467, 479, 499, 503, 523, 541, 547, 569, 593, 599, 607, 653, 659, 677, 757, 787, 797, 829, 853, 877, 907, 919, 947, 967, 971, 977, 1033

Offset: 1

Author

J. M. Bergot and Robert Israel, Nov 02 2020

Keywords

• nonn

Comments

Primes p such that -A049711(p)*A013632(p) mod p is prime.

Includes primes p such that p-8, p-2 and p+4 are also prime. Dickson's conjecture implies that there are infinitely many of these.

Examples

			a(3) = 19 is a member because 19 is prime, the previous and following primes are 17 and 23, and (17*23) mod 19 = 11 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013632, A049711, A338566, A338567.

Programs

Maple

R:= NULL: p:= 0: q:= 2: r:= 3:
count:= 0:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  if isprime(p*r mod q) then count:= count+1; R:= R, q;  fi;
od:
R;