Sophie Germain primes and involutions of ℤn×
نویسندگان
چکیده
منابع مشابه
Large Sophie Germain primes
If P is a prime and 2P+1 is also prime, then P is a Sophie Germain prime. In this article several new Sophie Germain primes are reported, which are the largest known at this time. The search method and the expected search times are discussed.
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The numbers 242206083 · 238880 ± 1 are twin primes. The number p = 2375063906985 · 219380 − 1 is a Sophie Germain prime, i.e. p and 2p + 1 are both primes. For p = 4610194180515 · 25056 − 1, the numbers p, p + 2 and 2p + 1 are all primes. In the first days of October, 1995, Harvey Dubner [4] found the largest known twin primes with 5129 decimal digits. (Our earlier twin prime record was 6970538...
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In this article we give a proof of Serre’s conjecture for the cases of odd conductor and even conductor semistable at 2, and arbitrary weight. Our proof in both cases will be unconditional: in particular, it will not depend on any yet unproved generalization of Kisin’s modularity lifting results to characteristic 2 (moreover, we will not consider at all characteristic 2 representations in any s...
متن کاملSGCM: The Sophie Germain Counter Mode
Sophie Germain Counter Mode (SGCM) is an authenticated encryption mode of operation, to be used with 128-bit block ciphers such as AES. SGCM is a variant of the NIST standardized Galois / Counter Mode (GCM) which has been found to be susceptible to weak key / short cycle forgery attacks. The GCM attacks are made possible by its extremely smooth-order multiplicative group which splits into 512 s...
متن کاملSophie Germain ’ s grand plan to prove Fermat ’ s Last Theorem
A study of Sophie Germain’s extensive manuscripts on Fermat’s Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the single theorem for Case 1 for which she is known from a published footnote by Legendre. Germain had a fully-fledged, highly developed, sophisticated plan of attack on Fermat’s Last Theorem. The supporting algorithms she i...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2015
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2015.8.653