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

Author

Jean-François Alcover, Apr 17 2016

Keywords

• nonn
• cons

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.

Crossrefs

Cf. A005597, A271951.

Programs

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

Formula

Equals A005597 / A271951.