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%I #5 Jan 02 2013 21:17:49
%S 97,193,263,311,337,383,457,503,647,673,839,887,937,1009,1033,1103,
%T 1223,1319,1487,1511,1583,1609,1777,1801,1823,1873,2017,2377,2423,
%U 2447,2593,2617,2687,2713,2903,2927,2999,3023,3049,3361,3407,3457,3623,3671
%N Primes the sum of four consecutive composite numbers.
%H Harvey P. Dale, <a href="/A060329/b060329.txt">Table of n, a(n) for n = 1..1000</a>
%t composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); a = {}; Do[ p = composite[ n ] + composite[ n + 1 ] + composite[ n + 2 ] + composite[ n + 3 ]; If[ PrimeQ[ p ], a = Append[ a, p ] ], {n, 1, 1000} ]; a
%t nn=1000;With[{comps=Complement[Range[2,nn],Prime[Range[PrimePi[ nn]]]]}, Select[ Total/@Partition[comps,4,1],PrimeQ]] (* _Harvey P. Dale_, Jan 02 2013 *)
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Mar 30 2001
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