Definition:Twin Primes Constant/Also defined as

Definition

François Le Lionnais and Jean Brette, in their Les Nombres Remarquables of $1983$, define the twin primes constant as:

\(\ds \Pi_2\)

\(:=\)

\(\ds 2 \prod_{\substack {p \mathop \ge 3 \\ \text {$p$ prime} } } \paren {1 - \dfrac 1 {\paren {p - 1}^2} }\)

\(\ds \)

\(\approx\)

\(\ds 1 \cdotp 32032 \, 36316 \ldots\)

This sequence is A114907 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Sources

• 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,32032 36316 \ldots$

• Weisstein, Eric W. "Twin Primes Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TwinPrimesConstant.html