A264736 Decimal expansion of Product_{p prime > 2} 1-1/(p^2-3p+3), a constant related to I. M. Vinogradov's proof of the "ternary" Goldbach conjecture.
5, 7, 3, 8, 1, 3, 8, 6, 2, 6, 1, 2, 0, 7, 0, 5, 9, 9, 0, 4, 7, 8, 8, 6, 3, 9, 3, 4, 5, 7, 9, 0, 6, 3, 2, 7, 6, 6, 4, 7, 7, 6, 1, 0, 9, 5, 5, 8, 6, 8, 7, 3, 8, 6, 2, 4, 8, 7, 0, 9, 3, 8, 7, 1, 4, 6, 2, 2, 4, 3, 8, 8, 5, 7, 6, 7, 0, 1, 3, 6, 8, 1, 9, 2, 8, 5, 4, 5, 7, 7, 5, 2, 8, 5, 2, 0, 6, 3, 0
Offset: 0
Examples
0.5738138626120705990478863934579063276647761095586873862487...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.1 Hardy-Littlewood Constants, p. 88.
Links
- Eric Weisstein's MathWorld, Goldbach's Conjecture.
- Eric Weisstein's MathWorld, Vinogradov's theorem.
- Wikipedia, Goldbach's conjecture.
- Wikipedia, Vinogradov's theorem.
Programs
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Mathematica
$MaxExtraPrecision = 600; digits = 99; terms = 600; P[n_] := PrimeZetaP[n] - 1/2^n; LR = LinearRecurrence[{6, -14, 15, -6}, {0, 0, -2, -9}, terms + 10]; r[n_Integer] := LR[[n]]; Exp[NSum[r[n]*P[n-1]/(n-1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits+10]] // RealDigits[#, 10, digits]& // First -
PARI
prodeulerrat(1-1/(p^2-3*p+3), 1, 3) \\ Amiram Eldar, Mar 11 2021