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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice
• changed

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.
• Thomas Bloom, Are there infinitely many primes p such that every even number n <= p-3 can be written as a difference of primes n = q_1 - q_2 where q_1, q_2 <= p?, Erdős Problems.
• Terence Tao, Erdős problem database, see entry no. 17.
• Eric Weisstein's World of Mathematics, Cluster Prime.
• Wikipedia, Cluster prime.
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A038134, A039506, A039507, A072325.

Programs

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, j0, AppendTo[lst, p[[i]]]]]; lst

Extensions

More terms from Christian G. Bower, Feb 15 1999