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11: 27.22 Software

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Maple. isprime combines a strong pseudoprime test and a Lucas pseudoprime test. ifactor uses cfrac (§27.19) after exhausting trial division. Brent–Pollard rho, Square Forms Factorization, and ecm are available also; see §27.19.

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Mathematica. PrimeQ combines strong pseudoprime tests for the bases 2 and 3 and a Lucas pseudoprime test. No known composite numbers pass these three tests, and Bleichenbacher (1996) has shown that this combination of tests proves primality for integers below ${10}^{16}$. Provable PrimeQ uses the Atkin–Goldwasser–Kilian–Morain Elliptic Curve Method to prove primality. FactorInteger tries Brent–Pollard rho, Pollard $p-1$, and then cfrac after trial division. See §27.19. ecm is available also, and the Multiple Polynomial Quadratic sieve is expected in a future release.

For additional Mathematica routines for factorization and primality testing, including several different pseudoprime tests, see Bressoud and Wagon (2000).

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12: Daniel W. Lozier

… … ► 1941 in Portland, Oregon) was the Group Leader of the Mathematical Software Group in the Applied and Computational Mathematics Division of NIST until his retirement in 2013. …

13: Bonita V. Saunders

… … ►Bonita V. Saunders, born in Portsmouth, Virginia, is a member of the Applied and Computational Mathematics Division of the Information Technology Laboratory at the National Institute of Standards and Technology. …

14: Charles W. Clark

… … ►He has served as Chair of the Division of Atomic, Molecular, and Optical Physics of the APS, Chair of the Physics Section of the AAAS, and as Program Manager for Atomic, Molecular, and Quantum Physics at the U. …

15: Philip J. Davis

… … ►At that time John Todd was Chief of the Numerical Analysis Section of the Applied Mathematics Division and head of the Computation Laboratory that co-developed, with the NBS Electronic Computer Laboratory, the Standards Eastern Automatic Computer (SEAC), the first fully operational stored-program electronic digital computer in the United States. … ►In 1961, Davis hired Frank W. J. Olver, a founding member of the Mathematics Division and Head of the Numerical Methods Section at the National Physical Laboratory, Teddington, U. … ►Davis left NBS in 1963 to become a faculty member in the Division of Applied Mathematics at Brown University, but during the early development of the DLMF, which started in 1998, he was invited back to give a talk and speak with DLMF project members about their plans. …

16: Leonard C. Maximon

… ►He had been an Assistant Professor in the Graduate Division of Applied Mathematics at Brown University, a Visiting Professor at the Norwegian Technical University in Trondheim, Norway, and a Physicist at the Center for Radiation Research at the National Bureau of Standards. …

17: 27.18 Methods of Computation: Primes

… ►For small values of $n$, primality is proven by showing that $n$ is not divisible by any prime not exceeding $\sqrt{n}$. …

18: 27.19 Methods of Computation: Factorization

… ►Trial division is one example. …

19: 26.18 Counting Techniques

… ►The number of positive integers $\le N$ that are not divisible by any of the primes $p_1,p_2,\mathrm{\dots },p_n$ (§27.2(i)) is …

20: Frank W. J. Olver

… ►In 1945–1961 he was a founding member of the Mathematics Division and Head of the Numerical Methods Section at the National Physical Laboratory, Teddington, U. …