On distribution of semiprime numbers. (English. Russian original) Zbl 1300.11093
Russ. Math. 58, No. 8, 43-48 (2014); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2014, No. 8, 53-59 (2014).
Summary: A semiprime is a natural number which is the product of two (possibly equal) prime numbers. Let \(y\) be a natural number and \(g(y)\) be the probability for a number \(y\) to be semiprime. In this paper we derive an asymptotic formula to count \(g(y)\) for large \(y\) and evaluate its correctness for different \(y\). We also introduce strongly semiprimes, i.e., numbers each of which is a product of two primes of large dimension, and investigate distribution of strongly semiprimes.
MSC:
| 11N25 | Distribution of integers with specified multiplicative constraints |
| 11N37 | Asymptotic results on arithmetic functions |
Keywords:
semiprime integer; strongly semiprime; distribution of semiprimes; factorization of integers; RSA ciphering methodSoftware:
OEISOnline Encyclopedia of Integer Sequences:
Semiprimes (or biprimes): products of two primes.Decimal expansion of constant B3 (or B_3) related to the Mertens constant.
Semiprimes p*q for which p <= q < p^3.
References:
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