

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

T. D. Noe, Cluster primes less than 10^6; table of n, a(n) for n = 1..8287
Richard Blecksmith, Paul Erdős and J. L. Selfridge, Cluster Primes, Amer. Math. Monthly, 106 (1999), 4348.
Eric Weisstein's World of Mathematics, Cluster Prime.
Index entries for sequences related to Goldbach conjecture


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

Cf. A038133, A039506, A039507, A072325.
Sequence in context: A240699 A065380 A211075 * A215697 A322184 A245072
Adjacent sequences: A038131 A038132 A038133 * A038135 A038136 A038137


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Christian G. Bower, Feb 15 1999


STATUS

approved



