Some Notes on the Distribution of Mersenne Primes

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Gaussian Mersenne and Eisenstein Mersenne primes

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....

متن کامل

Artin Reciprocity and Mersenne Primes

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...

متن کامل

On Using Mersenne Primes in Designing Cryptoschemes

The paper proposes justification of using Mersenne primes in the following cryptoschemes: commutative and publickey encryption algorithms and zero-knowledge protocol. The cryptoschemes are based on computational difficulty of finding discrete logarithm in the finite fields GF (2), where s is a sufficiently large prime such that 2s−1 is also a prime, for example s = 1279, s = 2203, and s = 4253.

متن کامل

Characterizations of Mersenne and 2-rooted primes

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

متن کامل

An elliptic curve test for Mersenne primes

Let l ≥ 3 be a prime, and let p = 2 − 1 be the corresponding Mersenne number. The Lucas-Lehmer test for the primality of p goes as follows. Define the sequence of integers xk by the recursion x0 = 4, xk = x 2 k−1 − 2. Then p is a prime if and only if each xk is relatively prime to p, for 0 ≤ k ≤ l − 3, and gcd(xl−2, p) > 1. We show, in the first section, that this test is based on the successiv...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Applied Mathematics

سال: 2010

ISSN: 2152-7385,2152-7393

DOI: 10.4236/am.2010.14041