largest known
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1: 27.22 Software
2: 27.12 Asymptotic Formulas: Primes
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►where depends only on , and is the Euler totient function (§27.2).
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►The largest known prime (2018) is the Mersenne prime .
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3: Errata
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Paragraph Prime Number Theorem (in §27.12)
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The largest known prime, which is a Mersenne prime, was updated from (2009) to (2018).
4: 27.19 Methods of Computation: Factorization
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►Deterministic algorithms are slow but are guaranteed to find the factorization within a known period of time.
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►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.
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►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.
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