

A038134


From a subtractive Goldbach conjecture: cluster primes.


9



3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 101, 103, 107, 109, 113, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 233, 239, 241, 271, 277, 281, 283, 311, 313, 317, 353, 359, 389, 401, 421, 433
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OFFSET

1,1


COMMENTS

Erdős asks if there are infinitely many primes p such that every even number <= p3 can be expressed as the difference between two primes each <= p.


REFERENCES

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


LINKS

Richard Blecksmith, Paul Erdős and J. L. Selfridge, Cluster Primes, Amer. Math. Monthly, 106 (1999), 4348.


MATHEMATICA

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


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



