A343683 Primes p1 such that the sum of 9 consecutive primes, p1+p2+p3+p4+p5+p6+p7+p8+p9, and the three sums (p1+p2+p3), (p4+p5+p6), (p7+p8+p9) are all prime numbers.

29, 83, 389, 1151, 2293, 2521, 2699, 2753, 4831, 7121, 9857, 12409, 13679, 24439, 25943, 36083, 43201, 47317, 49037, 49069, 49109, 51829, 51859, 53717, 61471, 64091, 68449, 70271, 77047, 87337, 87911, 90709, 111109, 113173, 114577, 117577, 117889, 118051, 128549, 134837, 149533, 172489

Offset: 1

Author

Zak Seidov, Apr 26 2021

Keywords

• nonn

Examples

			n=1, p1=29:
29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 = 401,
29 + 31 + 37 = 97, 41 + 43 + 47 = 131, 53 + 59 + 61 = 173, all primes.
		

Crossrefs

Cf. A082251 (primes that are the sum of 9 consecutive primes).

Programs

Mathematica

Select[Prime@Range@10000,And@@PrimeQ[Flatten@{Total[s=NextPrime[#,0~Range~8]],Total/@Partition[s,3]}]&] (* Giorgos Kalogeropoulos, Apr 26 2021 *)