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Properties of large prime divisors of numbers of the form p − 1 |
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| Authors: | M. A. Cherepnev |
| Affiliation: | (1) M. V. Lomonosov Moscow State University, Russia |
| Abstract: | The main result of this paper is the fact that the fraction of primes p ≤ 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. |
| Keywords: | prime number large prime divisor number of prime divisors Landau estimate for the Euler function Selberg method cryptographic protocol |
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