%I #12 May 17 2014 11:29:39
%S 17,31,311,17783
%N Smallest prime simultaneously the sum of two, three, ..., n consecutive composite numbers.
%C Next term is > 5000000. - Larry Reeves (larryr(AT)acm.org), Jan 03 2003
%C There are no more terms. If the sum of five consecutive composite numbers is not divisible by 2 or 5 then it is 7 or 23 modulo 30. The sum of six consecutive composite numbers cannot be 7 or 23 modulo 30. - _Jens Kruse Andersen_, May 11 2014
%e 17 = 8+9.
%e 31 = 15+16 = 9+10+12.
%e 311 = 155+156 = 102+104+105 = 76+77+78+80.
%e 17783 = 8891+8892 = 5926+5928+5929 = 4444+4445+4446+4448 = 3554+3555+3556+3558+3560.
%K nonn,fini,full
%O 2,1
%A _Robert G. Wilson v_, Mar 30 2001