By the fundamental theorem of arithmetic, every positive integer has a unique prime factorization. (By convention, 1 is the empty product.) Testing whether the integer is prime can be … 展开

In number theory, there are many integer factoring algorithms that heuristically have expected running time
in little-o 展开

The Schnorr–Seysen–Lenstra probabilistic algorithm has been rigorously proven by Lenstra and Pomerance to have expected running time Ln[⁠1/2⁠, … 展开

• msieve – SIQS and NFS – has helped complete some of the largest public factorizations known
• Richard P. Brent, "Recent Progress and Prospects for Integer Factorisation Algorithms", Computing and Combinatorics", 2000, pp. … 展开

Among the b-bit numbers, the most difficult to factor in practice using existing algorithms are those semiprimes whose factors are of similar size. … 展开

Special-purpose
A special-purpose factoring algorithm's running time depends on the properties of the number to be factored or on one of its unknown factors: size, special form, etc. The parameters which determine the running time vary among … 展开

• Aurifeuillean factorization
• Bach's algorithm for generating random numbers with their factorizations
• Canonical representation of a positive integer
• Factorization 展开