In mathematics, the Pocklington–Lehmer primality test is a primality test devised by Henry Cabourn Pocklington[1] and Derrick Henry Lehmer.[2]
The test uses a partial factorization of to prove that an integer is prime.
It produces a primality certificate to be found with less effort than the Lucas primality test, which requires the full factorization of .
^Pocklington, Henry C. (1914–1916). "The determination of the prime or composite nature of large numbers by Fermat's theorem". Proceedings of the Cambridge Philosophical Society. 18: 29–30. Retrieved 2022-06-22.
^D. H. Lehmer (1927). "Tests for primality by the converse of Fermat's theorem". Bull. Amer. Math. Soc. 33 (3): 327–340. doi:10.1090/s0002-9904-1927-04368-3.
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mathematics, the Pocklington–Lehmer primalitytest is a primalitytest devised by Henry Cabourn Pocklington and Derrick Henry Lehmer. The test uses a partial...
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P(6542) = 65521 for unsigned sixteen-bit integers. That would suffice to testprimality for numbers up to 655372 = 4,295,098,369. Preparing such a table (usually...
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v t e Number-theoretic algorithms Primalitytests AKS APR Baillie–PSW Elliptic curve Pocklington Fermat Lucas Lucas–Lehmer Lucas–Lehmer–Riesel Proth's...
above methods adapt easily to this application. This can be used for primalitytesting of large numbers n, for example. Pseudocode A recursive algorithm...
v t e Number-theoretic algorithms Primalitytests AKS APR Baillie–PSW Elliptic curve Pocklington Fermat Lucas Lucas–Lehmer Lucas–Lehmer–Riesel Proth's...
v t e Number-theoretic algorithms Primalitytests AKS APR Baillie–PSW Elliptic curve Pocklington Fermat Lucas Lucas–Lehmer Lucas–Lehmer–Riesel Proth's...
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