Abstract.
In the RSA cryptosystem integers of the form n = p · q with p and q primes of comparable size (‘RSA-integers’) play an important role. It is a folklore result of cryptographers that C r (x), the number of integers n ≤ x that are of the form n = pq with p and q primes such that p < q < rp, is for fixed r > 1 asymptotically equal to c r x log−2 x for some constant c r > 0. Here we prove this and show that c r = 2logr.
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Received: December 18, 2007. Revised: January 8, 2008.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Decker, A., Moree, P. Counting RSA-Integers. Result. Math. 52, 35–39 (2008). https://doi.org/10.1007/s00025-008-0285-5
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DOI: https://doi.org/10.1007/s00025-008-0285-5