| Input interpretation |
|---|
| prime factorization |
| Alternate names |
| integer factorization | prime decomposition |
| Basic definition |
| The factorization of a number into its constituent primes. Also called prime decomposition. |
| Detailed definition |
| The factorization of a number into its constituent primes, also called prime decomposition. Given a positive integer n>=2, the prime factorization is written n = p_1^(alpha_1) p_2^(alpha_2) …p_k^(alpha_k), where the p_is are the k prime factors, each of order alpha_i. Each factor p_i^(alpha_i) is called a primary. Prime factorization can be performed in the Wolfram Language using the command FactorInteger[n], which returns a list of (p_i, alpha_i) pairs. Through his invention of the Pratt certificate, Pratt became the first to establish that prime factorization lies in the complexity class NP. |
| Related topics |
| distinct prime factorization | distinct prime factors | economical number | equidigital number | factorization | ordered factorization | primary | prime factor | prime factorization algorithms | prime number | roundness | round number | wasteful number |
| Related Wolfram Language symbol |
| FactorInteger |
| Educational grade level |
| elementary school level (California grade 5 standard) |