A103523 Concatenations of pairs of primes that differ by 100.

3103, 7107, 13113, 31131, 37137, 67167, 73173, 79179, 97197, 127227, 139239, 151251, 157257, 163263, 181281, 193293, 211311, 283383, 331431, 349449, 367467, 379479, 409509, 421521, 457557, 463563, 487587, 499599, 541641, 547647, 577677

Offset: 1

Author

Jonathan Vos Post, Mar 21 2005

Keywords

• base
• easy
• nonn

Comments

Integers in this sequence can never be prime, as, starting from the second one, they are all multiples of 3.

Examples

			9191019 is in this sequence because 919 is prime, 919+100 = 1019 is prime and 9191019 is the concatenation of those two primes differing by 100.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..9832

Crossrefs

Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719.

Programs

Maple

f:= proc(n) if isprime(n) and isprime(n+100) then 10^(1+ilog10(n+100))*n+n+100 fi end proc:
map(f, [3,seq(i,i=7..1000,6)]); # Robert Israel, Dec 07 2015

Mathematica

FromDigits[Join@@IntegerDigits/@{#,#+100}]&/@Select[Prime@Range@200,PrimeQ[#+100]&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)

Python

from sympy import isprime, primerange as prange
def auptop(lim):
  return [int(str(p)+str(p+100)) for p in prange(2, lim+1) if isprime(p+100)]
print(auptop(577)) # Michael S. Branicky, Jul 04 2021

Formula

List: concatenate(p, p+100) iff p and p+100 are primes.