A103576 -id:A103576 - cp's OEIS frontend

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

Jonathan Vos Post, Mar 25 2005

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.

			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.

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

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

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

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

A104873 Concatenations of pairs of primes that differ by 10^12.

Original entry on oeis.org

611000000000061, 1631000000000163, 1931000000000193, 2111000000000211, 2711000000000271, 3311000000000331, 5471000000000547, 6611000000000661, 7511000000000751, 7871000000000787, 9971000000000997, 10511000000001051

Offset: 1

Jonathan Vos Post, Mar 29 2005

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(177) concatenated with Prime(37607912056) = 10511000000001051 = 3 * 3503666666667017.

			61 is prime, specifically prime(18) and 61 + 10^12 is prime, specifically prime(7607912020), so their concatenation is in this sequence: 611000000000061. The concatenation is not itself prime, as it equals 3 * 7 * 23 * 1265010351967.

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

Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719, A103523, A103534, A103576, A103617.

#*10^13+10^12+#&/@Select[Prime[Range[200]],PrimeQ[#+10^12]&] (* Harvey P. Dale, Jan 18 2021 *)

a(n) = Concatenate(P, P+10^12) iff P prime and P+10^12 prime.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula