Geodesic
Properties of large prime divisors of numbers of the form $p-1$
Matematičeskie zametki, Tome 80 (2006) no. 6, pp. 920-925.

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The main result of this paper is the fact that the fraction of primes $p\le x$ satisfying the condition that $p-1$ has a prime divisor $q>\exp(\ln x/\ln\ln x)$ and the number of prime divisors of $q-1$ essentially differ from $\ln\ln(x/n)$, where $n=(p-1)/q$, tends to zero as $x$ increases. 
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M. A. Cherepnev. Properties of large prime divisors of numbers of the form $p-1$. Matematičeskie zametki, Tome 80 (2006) no. 6, pp. 920-925. http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a9/

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