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

1,1

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.

Links

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A321284 A186095 A218397 * A213334 A211417 A287246

Adjacent sequences: A103614 A103615 A103616 * A103618 A103619 A103620

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Mar 25 2005

Status

approved