A356471 First of 5 consecutive primes p,q,r,s,t such that p*q+ q*r + r*s + s*t + t*p is prime.

19, 41, 47, 53, 157, 199, 491, 557, 563, 571, 647, 1063, 1091, 1097, 1109, 1163, 1171, 1217, 1259, 1279, 1361, 1367, 1487, 1601, 1621, 1753, 1901, 1951, 2053, 2161, 2383, 2441, 2549, 2777, 2851, 2879, 2887, 2953, 2957, 3041, 3061, 3067, 3163, 3191, 3491, 3499, 3719, 3881, 4003, 4007, 4013, 4093

Offset: 1

Author

J. M. Bergot and Robert Israel, Aug 08 2022

Keywords

• nonn

Examples

			a(3) = 47 is a term because 47, 53, 59, 61, 67 are 5 consecutive primes with 47*53 + 53*59 + 59*61 + 61*67 + 67*47 = 16453 prime.
		

Links

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

Crossrefs

Cf. A356475, A356477.

Programs

Maple

R:= NULL: count:= 0:
P:= Vector(5,ithprime):
while count < 100 do
  x:= P[1]*P[2]+P[2]*P[3]+P[3]*P[4]+P[4]*P[5]+P[5]*P[1];
  if isprime(x) then R:= R, P[1]; count:= count+1 fi;
  P[1..4]:= P[2..5];
  P[5]:= nextprime(P[5]);
od:
R;

Mathematica

Select[Partition[Prime[Range[600]], 5, 1], PrimeQ[Total[# * RotateLeft[#]]] &][[;; , 1]] (* Amiram Eldar, Aug 08 2022 *)

Python

from itertools import islice
from sympy import isprime, nextprime
def agen():
    p, q, r, s, t = 2, 3, 5, 7, 11
    while True:
        if isprime(p*q + q*r + r*s + s*t + t*p): yield p
        p, q, r, s, t = q, r, s, t, nextprime(t)
print(list(islice(agen(), 52))) # Michael S. Branicky, Aug 08 2022