A372082 Primes p such that the 10's complement A089186(p) and the concatenations of p and A089186(p) and of A089186(p) and p are all prime.

3, 7, 17, 29, 71, 83, 281, 719, 1637, 2309, 3701, 4493, 5507, 6299, 7691, 8363, 9029, 11003, 13163, 17117, 18371, 20807, 31181, 31793, 32693, 32843, 33617, 33893, 34211, 34673, 37277, 38453, 49409, 50591, 61547, 62723, 65327, 65789, 66107, 66383, 67157, 67307, 68207, 68819, 79193, 81629, 82883

Offset: 1

Author

Robert Israel, Jul 03 2024

Keywords

• nonn
• base

Comments

If p is a term and starts with 1 to 8, then its 10's complement A089186(p) is also a term. This is not the case if p starts with 9, as then A089186(A089186(p)) <> p. For example, 9029 is a term but its 10's complement 971 is not a term.

Examples

			a(3) = 17 is a term because 17 is a prime, its 10's complement 83 is a prime, and the concatenations 1783 and 8317 are primes.
		

Links

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

Crossrefs

Cf. A089186. Subset of A083989.

Programs

Maple

filter:= proc(n) local d,c;
if not isprime(n) then return false fi;
d:= 10^(1+ilog10(n)); c:= d-n;
isprime(c) and isprime(c*d+n) and isprime(n*10^(1+ilog10(c))+c)
end proc:
select(filter, [seq(i,i=3..10000,2)]);