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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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.
• Wikipedia, Cluster prime.
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A038133, 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, j
				

Extensions

More terms from Christian G. Bower, Feb 15 1999