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- Title
Products of two proportional primes.
- Authors
Moree, Pieter; Eddin, Sumaia Saad
- Abstract
In RSA cryptography numbers of the form , with and two distinct proportional primes play an important role. For a fixed real number we formalize this by saying that an integer is an RSA-integer if and are primes satisfying . Recently Dummit, Granville and Kisilevsky showed that substantially more than a quarter of the odd integers of the form up to , with both prime, satisfy . In this paper, we investigate this phenomenon for RSA-integers. We establish an analogue of a strong form of the prime number theorem with the logarithmic integral replaced by a variant. From this we derive an asymptotic formula for the number of RSA-integers which is much more precise than an earlier one derived by Decker and Moree in 2008.
- Subjects
PRIME numbers; CRYPTOGRAPHY; INTEGERS; PRIME number theorem; ODD numbers; LOGARITHMIC integrals
- Publication
International Journal of Number Theory, 2017, Vol 13, Issue 10, p2583
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042117501445