♦ 5 matching pages ♦
5 matching pages
… ►where depends only on , and is the Euler totient function (§27.2). … ►The largest known prime (2018) is the Mersenne prime . …
Paragraph Prime Number Theorem (in §27.12)
The largest known prime, which is a Mersenne prime, was updated from (2009) to (2018).
… ►Deterministic algorithms are slow but are guaranteed to find the factorization within a known period of time. … ►As of January 2009 the largest prime factors found by these methods are a 19-digit prime for Brent–Pollard rho, a 58-digit prime for Pollard , and a 67-digit prime for ecm. … ►As of January 2009 the snfs holds the record for the largest integer that has been factored by a Type II probabilistic algorithm, a 307-digit composite integer. …The largest composite numbers that have been factored by other Type II probabilistic algorithms are a 63-digit integer by cfrac, a 135-digit integer by mpqs, and a 182-digit integer by gnfs. …