A339866 Primes that are simultaneously the sums of 11, 13, and 15 consecutive primes.

8472193, 14084311, 16569827, 28358851, 33546551, 45993127, 91174081, 123593753, 186861293, 205286087, 224010023, 227568853, 310359607, 335497667, 423104119, 454320901, 482749429, 492404317, 558048187, 560997023, 566428813, 700508971, 707060359, 715731761, 735276379

Offset: 1

Author

Zak Seidov, Apr 24 2021

Keywords

• nonn

Comments

Intersection of A127340, A127341, A161612.

The first case with 17 consecutive primes is a(219) = 8410721789. Are there more such terms?

a(10) = 205286087 is the sum of k consecutive primes not only for k = 11, 13, and 15, but also for k=1 (i.e., a(10) is a prime), k=9, and k=233. - Jon E. Schoenfield, Apr 24 2021

Examples

			Sum_{k=61746..61756} prime(k) = Sum_{k=52937..52949} prime(k) = Sum_{k=46425..46439} prime(k) = 8472193, so 8472193 is a term. - _Jon E. Schoenfield_, Apr 24 2021
		

Crossrefs

Cf. A127340, A127341, A161612, A213914.

Programs

Mathematica

Module[{nn=4*10^6,prs,p11,p13,p15},prs=Prime[Range[nn]];p11=Total/@Partition[prs,11,1];p13=Total/@Partition[prs,13,1]; p15=Total/@ Partition[ prs,15,1];Select[Intersection[ p11,p13,p15],PrimeQ]] (* Harvey P. Dale, Aug 14 2023 *)