%I #19 Jan 12 2016 03:11:24
%S 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,
%T 101,103,107,109,113,131,137,139,151,157,163,167,173,179,181,193,197,
%U 199,233,239,241,271,277,281,283,311,313,317,353,359,389,401,421,433
%N From a subtractive Goldbach conjecture: cluster primes.
%C Erdős asks if there are infinitely many primes p such that every even number <= p-3 can be expressed as the difference between two primes each <= p.
%D R. K. Guy, Unsolved Problems In Number Theory, section C1.
%H T. D. Noe, <a href="/A038134/b038134.txt">Cluster primes less than 10^6; table of n, a(n) for n = 1..8287</a>
%H Richard Blecksmith, Paul Erdős and J. L. Selfridge, <a href="http://www.jstor.org/stable/2589585">Cluster Primes</a>, Amer. Math. Monthly, 106 (1999), 43-48.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClusterPrime.html">Cluster Prime.</a>
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%t m=1000; lst={}; n=PrimePi[m]-1; p=Table[Prime[i+1], {i, n}]; d=Table[0, {m/2}]; For[i=2, i<=n, i++, For[j=1, j<i, j++, diff=p[[i]]-p[[j]]; d[[diff/2]]++ ]; c=Count[Take[d, (p[[i]]-3)/2], 0]; If[c==0, AppendTo[lst, p[[i]]]]]; lst
%Y Cf. A038133, A039506, A039507, A072325.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Christian G. Bower_, Feb 15 1999