A104719 Concatenations of pairs of primes that differ by 10.

313, 717, 1323, 1929, 3141, 3747, 4353, 6171, 7383, 7989, 97107, 103113, 127137, 139149, 157167, 163173, 181191, 223233, 229239, 241251, 271281, 283293, 307317, 337347, 349359, 373383, 379389, 409419, 421431, 433443, 439449, 457467, 499509

Offset: 1

Author

Jonathan Vos Post and Parthasarathy Nambi, Mar 20 2005

Keywords

• base
• easy
• nonn

Comments

There are no primes in this sequence after a(1) = 313, as all values thereafter are divisible by 3. Semiprimes in this sequence include: a(2) = 717 = 3 * 239, a(4) = 1929 = 3 * 643, a(6) = 3747 = 3 * 1249, a(7) = 4353 = 3 * 1451, a(10) = 7989 = 3 * 2663, a(11) = 97107 = 3 * 32369, a(13) = 127137 = 3 * 42379, a(17) = 181191 = 3 * 60397, a(18) = 223233 = 3 * 74411, a(29) = 421431 = 3 * 140477, a(30) = 433443 = 3 * 144481, a(34) = 547557 = 3 * 182519, a(35) = 577587 = 3 * 192529, a(40) = 691701 = 3 * 230567, a(41) = 709719 = 3 * 236573, a(49) = 919929 = 3 * 306643, a(52) = 10091019 = 3 * 3363673.

Examples

			Primes 3 and 13 differ by 10.
		

Links

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

Crossrefs

Cf. A000040, A001358, A023202, A103195, A103206, A104718.

Programs

Mathematica

FromDigits[Join[IntegerDigits[#],IntegerDigits[#+10]]]&/@Select[ Prime[ Range[ 100]], PrimeQ[ #+10]&] (* Harvey P. Dale, Jun 14 2015 *)

Formula

a(n) = A023203(n) concatenated with A023203(n)+10.