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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 26 22:42 EDT 2019. Contains 321565 sequences. (Running on oeis4.)