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

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

Offset

1,1

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

Links

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A172601 A086438 A261149 * A297450 A172585 A336968

Adjacent sequences: A104870 A104871 A104872 * A104874 A104875 A104876

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Mar 29 2005

Status

approved