Quadratic Sieve Smoothness Calculator

About this calculator

The quadratic sieve smoothness calculator trial-divides an integer n by every prime up to a chosen smoothness bound B, reports whether n is B-smooth (meaning all of its prime factors are ≤ B), and returns the full prime factorization along with the largest prime factor found. If any factor above B remains after dividing out all primes ≤ B, n is not B-smooth.

Smoothness testing is the core screening step inside integer-factorization algorithms like the quadratic sieve and the general number field sieve, which don't try to factor a huge composite n directly — instead they search for many numbers related to n that happen to be B-smooth, then combine those relations with linear algebra to extract a factor. Cryptographers, number theory students, and researchers studying RSA-key factorization difficulty use this calculator to check smoothness on individual candidates and understand why a well-chosen key size keeps factoring computationally infeasible.