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%I #16 Aug 14 2023 15:25:17
%S 8472193,14084311,16569827,28358851,33546551,45993127,91174081,
%T 123593753,186861293,205286087,224010023,227568853,310359607,
%U 335497667,423104119,454320901,482749429,492404317,558048187,560997023,566428813,700508971,707060359,715731761,735276379
%N Primes that are simultaneously the sums of 11, 13, and 15 consecutive primes.
%C Intersection of A127340, A127341, A161612.
%C The first case with 17 consecutive primes is a(219) = 8410721789. Are there more such terms?
%C 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
%e 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
%t 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 *)
%Y Cf. A127340, A127341, A161612, A213914.
%K nonn
%O 1,1
%A _Zak Seidov_, Apr 24 2021
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