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From a subtractive Goldbach conjecture: odd primes that are not cluster primes.
5

%I #21 Dec 21 2021 23:48:37

%S 97,127,149,191,211,223,227,229,251,257,263,269,293,307,331,337,347,

%T 349,367,373,379,383,397,409,419,431,457,479,487,499,521,541,547,557,

%U 563,569,587,593,599,631,641,673,691,701,709,719,727,733,739,743,751

%N From a subtractive Goldbach conjecture: odd primes that are not 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. Sequence gives primes not having this property.

%D R. K. Guy, Unsolved Problems In Number Theory, section C1.

%H T. D. Noe, <a href="/A038133/b038133.txt">Table of n, a(n) for n = 1..10000</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. A038134, A039506, A039507, A072325.

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Christian G. Bower_, Feb 15 1999