%I #17 Mar 13 2018 12:35:51

%S 16344247,16588633,16711217,17416457,17700139,17806721,17860039,

%T 17895613,18091313,18144727,18483739,18573209,18698791,19040773,

%U 19384609,19529849,19620719,19748129,19784543,19802759,20421971,20476777,20531593,20806141,21283169,21356563

%N Primes that are the sum of 2001 consecutive primes.

%C Corresponding initial terms of 2001-tuples: 7, 61, 97, 313, 419, 449, 463, 479, 563, 577, 691, 733, 773, 911, 1039, 1093, 1123, 1187, 1201, 1213, 1459, 1483, 1493, 1607. The indices of these primes: 4, 18, 25, 65, 81, 87, 90, 92, 103, 106, 125, 130, 137, 156, 175, 183, 188, 195, 197, 198, 232, 235, 238, 253. - _Zak Seidov_, Feb 27 2013

%H Syed Iddi Hasan, <a href="/A216004/b216004.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = sum(prime(k), k = 4..2004), a(2) = sum(prime(k), k = 18..2018),... - _Zak Seidov_, Feb 27 2013

%t m = 2001; a = 2; b = Prime[m]; s = Sum[Prime[k], {k, m}]; Reap[Do[If[PrimeQ[s], Sow[s]]; b = NextPrime[b]; s = s - a + b; a = NextPrime[a], {m}]][[2, 1]] (* _Zak Seidov_, Feb 27 2013 *)

%t Select[Total/@Partition[Prime[Range[2500]],2001,1],PrimeQ] (* _Harvey P. Dale_, Mar 13 2018 *)

%Y Cf. A070934, A082244, A215991.

%K nonn

%O 1,1

%A _Syed Iddi Hasan_, Aug 30 2012