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table.yaml
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table.yaml
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ID: INPUT{id.yaml}
Title: Twin prime constant $C_2$
Definition: >
$C_2 := \prod_{p \geq 3} \big( 1 - (p-1)^{-2} \big)$,
where the product ranges over the odd primes $p$.
Parameters:
Comments:
comment-first-Hardy-Littlewood-conjecture: >
Let $\pi_2(x)$ denote the number of primes $p\leq x$ such that
$p+2$ is also a prime.
The first Hardy-Littlewood conjecture implies that
$\pi_2(x) \sim 2C_2\frac{x}{\log^2 x}$.
Formulas:
Programs:
References:
Links:
OEIS:
title: "OEIS: A005597"
url: https://oeis.org/A005597
Wiki:
title: "Wikipedia: First Hardy-Littlewood conjecture"
url: https://en.wikipedia.org/wiki/Twin_prime#First_Hardy%E2%80%93Littlewood_conjecture
Similar tables:
Keywords:
Tags:
- number theory
- probability theory
Data properties:
type: R
Display properties:
number-header: $C_2$
Numbers:
- 0.660161815846869573927812110014555778432623360284733413319448423335405642304495277143760031413839867911779