منابع مشابه
All Elite Primes Up to 250 Billion
A prime number p is called elite if only finitely many Fermat numbers 2 n + 1 are quadratic residues of p. Previously only the interval up to 10 was systematically searched for elite primes and 16 such primes were found. We extended this research up to 2.5 · 10 and found five further elites, among which 1 151 139 841 is the smallest and 171 727 482 881 the largest.
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We report on a joint project with Joe Buhler, Richard Crandall, Reijo Ernvall, and Tauno Metss ankyll a dealing with the computation of irregular primes and cyclo-tomic invariants for primes between four and eight million. This extends previous computations of Buhler et al. 4]. Our computation of the irregular primes is based on a new approach which has originated in the study of Stickelberger ...
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It is well-known that there are infinitely many irregular primes. We prove a quantitative version of this statement, namely the number of such primes p ≤ x is at least (1 + o(1)) log log x/ log log log x as x → ∞. We show that the same conclusion holds for the irregular primes corresponding to the Euler numbers. Under some conditional results from diophantine approximation, the above lower boun...
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Road block: Economists predict that there will be two billion motor vehicles on the roads by 2030, as private vehicle ownership spreads to the developing world. The image shows an urban motorway in Beijing, China. (Photo: Bev Sykes.) From the sheer amount of bad news coming through the 24/7 news cycle, one may get the impression that the world is on the road to apocalypse. To counter this impre...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2017
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3211