A340126 Primes p1 such that, with p2, p3, p4 the next three primes, p1*p2+p3*p4+p1, p1*p2+p3*p4+p2, p1*p2+p3*p4+p3 and p1*p2+p3*p4+p4 are all prime.

61751, 79393, 754991, 768373, 934393, 999529, 1575031, 1666019, 2512561, 3158069, 3434089, 3658607, 3815641, 3883967, 4063547, 4161721, 4390489, 5009737, 5539949, 5701019, 6475223, 6604691, 6736297, 7164757, 8194651, 8395997, 8440331, 9755821, 10003223

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Example

a(1) = 61751 is a term because with p1 = 61751, p2 = 61757, p3 = 61781, p4 = 61813, we have p1*p2+p3*p4+p1 = 7632487211, p1*p2+p3*p4+p2 = 7632487217, p1*p2+p3*p4+p3 = 7632487241, p1*p2+p3*p4+p4 = 7632487273, all primes.

Maple

p2:=2: p3:= 3: p4:= 5: count:= 0: R:= NULL:
while count < 10 do
  p1:= p2; p2:= p3; p3:= p4; p4:= nextprime(p4);
  w:= p1*p2+p3*p4;
  if andmap(t -> isprime(t+w), [p1, p2, p3, p4]) then
    count:= count+1; R:= R, p1
  fi
od:
R;

Crossrefs

Sequence in context: A340438 A253613 A257749 * A112015 A234864 A128879

Adjacent sequences: A340123 A340124 A340125 * A340127 A340128 A340129

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 29 2020

Extensions

a(11)-a(29) from Jon E. Schoenfield, Dec 29 2020

Status

approved