Mersenne primes, polygonal anomalies and string theory classification
نویسندگان
چکیده
منابع مشابه
Mersenne Primes, Polygonal Anomalies and String Theories Classification
It is pointed out that the Mersenne primes Mp = (2 p − 1) and associated perfect numbers Mp = 2 p−1 Mp play a significant role in string theory; this observation may suggest a classification of consistent string theories. Typeset using REVTEX 1 Anomalies and their avoidance have provided a guidepost in constraining viable particle physics theories. From the standard model to superstrings, the i...
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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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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...
متن کاملOverpseudoprimes, Mersenne Numbers and Wieferich Primes
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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ژورنال
عنوان ژورنال: Physical Review D
سال: 1999
ISSN: 0556-2821,1089-4918
DOI: 10.1103/physrevd.60.087901