# Quasi-prime number

From Encyclopedia of Mathematics

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.

#### Comments

See also Prime number; Distribution of prime numbers.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Quasi-prime_number&oldid=53937

This article was adapted from an original article by B.M. Bredikhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article