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

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

Offset: 1

Author

Jonathan Vos Post, Mar 29 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(177) concatenated with Prime(37607912056) = 10511000000001051 = 3 * 3503666666667017.

Examples

			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.
		

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, A103617.

Programs

Mathematica

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

Formula

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