Strong Twin Prime Conjecture/Mistake

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Source Work

1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables:

Thème et variations
$1,32032 36316 \ldots$


Mistake

Un argument probabiliste montre que, s'il existe une infinité de nombres premiers jumeaux, alors de nombre de ceux qui sont situés dans l'intervalle $\sqbrk {x, x + a}$ est de l'ordre de $C \cdot \dfrac a {\paren {\Log x}^2}$ avec $C = 1,32 \ldots$


In English:

A probabilistic argument shows that, if there exists an infinite number of twin primes, then the number of those which are situated in the interval $\closedint x {x + a}$ est of the order of $C \cdot \dfrac a {\paren {\Log x}^2}$ where $C = 1,32 \ldots$


Correction

This appears to be a misrepresentation of the Strong Twin Prime Conjecture.

Unless its thrust has been misunderstood, it would appear that in the limit, the number of twin primes in the interval $\closedint x x$ is of the order of $\dfrac {C x} {\paren {\Log x}^2}$, which does not seem to make sense.



Sources