Results 71 to 80 of about 125 (118)
Artin reciprocity and Mersenne primes
, 2000 From its conception in the work of Kronecker and Hilbert until Takagi's great paper of 1920, class field theory was developed in order to prove reciprocity laws. When Artin succeeded in proving his reciprocity law in 1927, however, its role changed dramatically, and soon afterwards it became a cornerstone of class field theory.
Lenstra, H.W., Stevenhagen, P.
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The Impact of Mersenne Primes on the Perfection of Numbers
Abstract:This research introduces a novel structural perspective on even perfect numbers, moving beyond the classical summation definition toward an "Anatomy of Disintegration." The study proposes that perfection is an absolute settlement between four internal pillars: the Dividend, the Divisor, the Result, and the inherent "Numerical Potential" (Baza ...
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The Mersenne Chain Reactor: A Physical Saturation Law for Mersenne Primes
Abstract The search for Mersenne primes at astronomical scales has reached a physical bottleneck: as numbers grow, the energy and time required for arithmetic verification become prohibitive on classical processors. Here we report a fundamental paradigm shift in the physics of computation and information.
Moustafa Ibrahim +2 more
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On prime divisors of Mersenne numbers [PDF]
Acta Arithmetica, 1991 Carl Pomerance, Péter Kiss, Paul Erdős
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There Are Infinitely Many Mersenne Primes
This paper explores Mersenne primes of the form 2p-1 where, p is a prime. By extension, the paper also explores Perfect numbers. An insight into these numbers is explored using novel methods that involve the trigonometric functions with integer factorable arguments.
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A Note on the Decimal Expansion of Reciprocals of Mersenne Primes
The aim of this note is to study, in the realm of Midy's theorem, arithmetic properties of digital blocks in the base-10 expansion of \(1 / M_p\), with \(M_p=2^p-1\) a Mersenne prime. If \(p\) divides the period length \(L\) of \(1/M_p\), one can partition the periodic part into \(p\) blocks, each of length \(\ell\).
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SeMA Journal, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Azizul Hoque +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Azizul Hoque +2 more
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