Explicit primality criteria for $(p-1)p^n-1$
نویسندگان
چکیده
منابع مشابه
Explicit primality criteria for (p-1)pn - 1
Deterministic polynomial time primality criteria for 2n − 1 have been known since the work of Lucas in 1876–1878. Little is known, however, about the existence of deterministic polynomial time primality tests for numbers of the more general form Nn = (p − 1) pn − 1, where p is any fixed prime. When n > (p − 1)/2 we show that it is always possible to produce a Lucas-like deterministic test for t...
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As a direct generalization of the Lucas-Lehmer test for the Mersenne numbers 2−1, explicit primality tests for numbers of the form N = h ·3 ±1 are derived, for fixed h, and all k with 3 > h. The result is that N is prime if and only if wk−1 ≡ ±1 mod N , where w is given by the recursion wj = wj−1(w 2 j−1 −3); the main difference with the original Lucas-Lehmer test is that the starting value w0 ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2000
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-00-01212-6