A342771 Primes p such that p, x+y, x-y, p-x*y and p+x*y are prime, where y = p mod 5 and x = (p-y)/5.

43, 53, 79, 103, 227, 769, 977, 1303, 2179, 2803, 3019, 5179, 5503, 8089, 8101, 10651, 10789, 13339, 13729, 14419, 16069, 17053, 17341, 18077, 23203, 25111, 26153, 26161, 32839, 34127, 34351, 34519, 38791, 39103, 44027, 54319, 56629, 57503, 59053, 60811, 62869, 63079, 64579, 64591, 65203, 69019

Offset

1,1

Comments

If y = 4, x+y = p-x*y.

Links

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

Example

a(3) = 79 is a term because y = 79 mod 5 = 4, x = (79-4)/5 = 15, and 15-4 = 11. 15+4 = 19, 79-4*15 = 19 and 79+4*15 = 139 are prime.

Maple

filter:= proc(n) local a, b;
  b:= n mod 5;
  a:= (n-b)/5;
  isprime(a+b) and isprime(a-b) and isprime(n-a*b) and isprime(n+a*b)
end proc:
select(filter, [seq(ithprime(i), i=1..1000)]);

Crossrefs

Sequence in context: A156252 A364689 A306627 * A174818 A280388 A180546

Adjacent sequences: A342768 A342769 A342770 * A342772 A342773 A342774

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 21 2021

Status

approved