Three New Mersenne Primes and a Statistical Theory
نویسندگان
چکیده
منابع مشابه
Three New Mersenne Primes and a Statistical Theory
If p is prime, Mp = 2P — 1 is called a Mersenne number. If ui = 4 and «<+1 = Mj+i — 2, then M„ is prime if and only if uv-i m 0(mod Mp). This is called the Lucas test (see Lehmer [4]). The primes Mom , M mi, and Mu2W which are now the largest known primes, were discovered by Illiac II at the Digital Computer Laboratory of the University of Illinois. The computing times were 1 hour 23 minutes, 1...
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The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem. Other properties of Gaussian Mersenne norms that contribute to the search for large primes are given....
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On March 3, 1998, the centenary of Emil Artin was celebrated at the Universiteit van Amsterdam. This paper is based on the two morning lectures, enti-tled`Artin reciprocity and quadratic reciprocity' and`Class eld theory in practice', which were delivered by the authors. It provides an elementary introduction to Artin reciprocity and illustrates its practical use by establishing a recently obse...
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We introduce a new class of pseudoprimes-so called ”overpseudoprimes” which is a special subclass of super-Poulet pseudoprimes. Denoting via h(n) the multiplicative order of 2 modulo n,we show that odd number n is overpseudoprime if and only if the value of h(n) is invariant of all divisors d > 1 of n. In particular, we prove that all composite Mersenne numbers 2 − 1, where p is prime, and squa...
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Article history: Received 18 June 2014 Received in revised form 11 June 2015 Accepted 12 June 2015 Available online 22 June 2015 Communicated by Neal Koblitz MSC: primary 11A41, 11A07 secondary 15B99, 05C90
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1964
ISSN: 0025-5718
DOI: 10.2307/2003409