A038134 From a subtractive Goldbach conjecture: cluster primes.

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

Offset

1,1

Comments

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.

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), 43-48.

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