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%I #12 Sep 17 2023 01:02:19
%S 5,23,31,41,53,59,67,71,83,97,101,109,131,139,173,181,197,199,211,223,
%T 233,251,263,269,271,281,311,331,349,353,373,401,421,431,439,443,449,
%U 457,463,487,491,499,503,523,563,587,593,607,617,631,647,659,661,677
%N Primes which are the sum of a prime number of consecutive primes.
%e 5 = 2 + 3.
%e 23 = 5 + 7 + 11.
%e 31 = 7 + 11 + 13.
%e 41 = 11 + 13 + 17.
%e 53 = 5 + 7 + 11 + 13 + 17.
%t lst={};Do[s=Prime[m];k=1;Do[p=Prime[n];s+=p;k++;If[PrimeQ[s]&&PrimeQ[k],If[s<=10837,AppendTo[lst,s]]],{n,m+1,5*5!}],{m,5*5!}];lst=Take[Union@lst,500] (* _Vladimir Joseph Stephan Orlovsky_, Sep 13 2009 *)
%t Module[{nn=60,prs},prs=Prime[Range[nn]];Take[Select[Union[ Flatten[ Table[ Total/@ Partition[prs,n,1],{n,prs}]]],PrimeQ],nn]] (* _Harvey P. Dale_, Aug 12 2016 *)
%Y Cf. A001043, A034707, A034962, A034965, A138591.
%K nonn
%O 1,1
%A _Henry Bottomley_, Dec 07 2001
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