A244186 Primes which are the concatenation of five consecutive primes p, q, r, s, t while the sum (p + q + r + s + t) is another prime.

711131719, 5359616771, 6771737983, 149151157163167, 401409419421431, 479487491499503, 757761769773787, 14091423142714291433, 18111823183118471861, 21132129213121372141, 26892693269927072711, 27192729273127412749, 36133617362336313637, 37613767376937793793

Offset: 1

Author

K. D. Bajpai, Jun 21 2014

Keywords

• nonn
• base

Comments

Subsequence of A086041.

Numbers: Concatenation of 5 consecutive primes at A132905.

Examples

			711131719 is in the sequence because the concatenation of [7, 11, 13, 17, 19] = 711131719 which is prime. The sum [7 + 11 + 13 + 17 + 19] = 67 is another prime.
5359616771 is in the sequence because the concatenation of [53, 59, 61, 67, 71] = 5359616771 which is prime. The sum [53 + 59 + 61 + 67 + 71] = 311 is another prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1703

Crossrefs

Cf. A000040, A086041, A034961, A034962, A132903, A244163.

Programs

Mathematica

FromDigits[Flatten[IntegerDigits/@#]]&/@Select[Partition[Prime[Range[ 1000]],5,1],AllTrue[{Total[#],FromDigits[Flatten[ IntegerDigits/@ #]]}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 24 2014 *)