A class of primality tests for trinomials which includes the Lucas-Lehmer test
نویسندگان
چکیده
منابع مشابه
Note on the Lucas–Lehmer Test
A proof of the Lucas–Lehmer test can be difficult to find, for most textbooks that state the result do not prove it. Over the past two decades, there have been some efforts to produce elementary versions of this famous result. However, the two that we acknowledge in this note did so by using either algebraic numbers or group theory. It also appears that in the process of trying to develop an el...
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The Lucas-Lehmer test provides a deterministic algorithm for testing whether, for a prime number p, Mp = 2−1 is also a prime number. The current work demonstrates that this test can be effectively implemented on a parallel graphics processing unit (GPU). The parallelization was achieved by two main parallel methods: (1) fast multiplication using parallel Fast Fourier transforms in extended prec...
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In 1876, E. Lucas showed that a quick proof of primality for a prime p could be attained through the prime factorization of p − 1 and a primitive root for p. V. Pratt’s proof that PRIMES is in NP, done via Lucas’s theorem, showed that a certificate of primality for a prime p could be obtained in O(log p) modular multiplications with integers at most p. We show that for all constants C ∈ R, the ...
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15 صفحه اولOn the implementation of AKS-class primality tests
Algorithms of the new “cyclotomic AKS class” determine rigorously and in polynomial time whether an input integer is prime. Herein are discussed implementation issues, with a focus on techniques such as asymptotically fast polynomial manipulations, the possible use of floating-point arithmetic, and special powering ladders. We implemented various of the ideas herein on an Apple G4, Mac OS X sys...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1982
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1982.98.477