Quasi-prime number

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A positive integer without small prime factors. This means that all prime factors of $n$ must be greater than $\mathcal P(n)$, where $\mathcal P(n)$ is a function that increases more slowly than $n$. For example,

$$\mathcal P(n)=n^{1/(\ln\ln n)^2}.$$

Quasi-prime numbers are well distributed in arithmetic progressions with large modulus.


See also Prime number; Distribution of prime numbers.


[a1] Diamond, Harold G.; Halberstam, H.; Galway, William F. "A higher-dimensional sieve method. With procedures for computing sieve functions" Cambridge Tracts in Mathematics 177. Cambridge University Press (2008). ISBN 978-0-521-89487-6 Zbl 1207.11099
How to Cite This Entry:
Quasi-prime number. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by B.M. Bredikhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article