A038133 From a subtractive Goldbach conjecture: odd primes that are not cluster primes.

97, 127, 149, 191, 211, 223, 227, 229, 251, 257, 263, 269, 293, 307, 331, 337, 347, 349, 367, 373, 379, 383, 397, 409, 419, 431, 457, 479, 487, 499, 521, 541, 547, 557, 563, 569, 587, 593, 599, 631, 641, 673, 691, 701, 709, 719, 727, 733, 739, 743, 751

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. Sequence gives primes not having this property.

References

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

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

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. A038134, A039506, A039507, A072325.

Sequence in context: A078494 A139980 A140830 * A144325 A234101 A161367

Adjacent sequences: A038130 A038131 A038132 * A038134 A038135 A038136

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Christian G. Bower, Feb 15 1999

Status

approved