A103617 Concatenations of pairs of primes that differ by 10^9.

71000000007, 971000000097, 1031000000103, 1811000000181, 2231000000223, 2411000000241, 2711000000271, 3491000000349, 4091000000409, 4331000000433, 4391000000439, 6071000000607, 6131000000613, 7871000000787, 8291000000829

Offset: 1

Author

Jonathan Vos Post, Mar 25 2005

Keywords

• base
• easy
• nonn

Comments

Integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for Prime(42) concatenated with Prime(50847544) = 1811000000181 = 3 x 603666666727.

Examples

			181 is prime, 181+10^9 = 1000000181 is prime, so their concatenation is an element of this sequence: 1811000000181. Coincidentally, prime(181)+10^9 = 1000001087 is also prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719, A103523, A103534, A103576.

Programs

Mathematica

FromDigits[Join[IntegerDigits[#],IntegerDigits[#+10^9]]]&/@Select[Prime[ Range[ 200]],PrimeQ[ #+ 10^9]&] (* Harvey P. Dale, May 14 2022 *)

Formula

a(n) = Concatenate(P, P+1000000000) iff P prime and P+1000000000 prime.