منابع مشابه
ON THE PRIMALITY OF n ! ±
For each prime p, let p# be the product of the primes less than or equal to p. We have greatly extended the range for which the primality of n!± 1 and p#± 1 are known and have found two new primes of the first form (6380! + 1, 6917!− 1) and one of the second (42209# + 1). We supply heuristic estimates on the expected number of such primes and compare these estimates to the number actually found.
متن کاملExplicit 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...
متن کاملEXPLICIT PRIMALITY CRITERIA FOR h • 2 k ± 1
Algorithms are described to obtain explicit primality criteria for integers of the form h • 2k ± 1 (in particular with h divisible by 3) that generalize classical tests for 2k ± 1 in a well-defined finite sense. Numerical evidence (including all cases with h < 105) seems to indicate that these finite generalizations exist for every h , unless h = Am 1 for some m , in which case it is proved the...
متن کاملNew Primality Criteria and Factorizations of 2 TM d = 1
A collection of theorems is developed for testing a given integer N for primality. The first type of theorem considered is based on the converse of Fermât 's theorem and uses factors of N — 1. The second type is based on divisibility properties of Lucas sequences and uses factors of N + 1. The third type uses factors of both N — 1 and N + 1 and provides a more effective, yet more complicated, p...
متن کاملThe primality of 2 h · 3 n − 1
We consider Williams’ primality test for rational integers of the form 2h ·3n−1. We give an algebraic proof of the test, and we resolve a sign ambiguity. We also show that the conditions of the original test can be relaxed, especially if h is divisible by a power of 2.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Missouri Journal of Mathematical Sciences
سال: 2008
ISSN: 0899-6180
DOI: 10.35834/mjms/1316032810