A Problem on the Conjecture concerning the Distribution of Generalized Fermat Prime Numbers (a New Method for the Search for Large Primes)
نویسنده
چکیده
Is it possible to improve the convergence properties of the series for the computation of the Cn involved in the distribution of the generalized Fermat prime numbers? If the answer to this question is yes, then the search for a large prime number P will be C · log(P ) times faster than today, where C ≈ 0.01.
منابع مشابه
Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs
Great strides have been made in recent years in the search for ever larger prime Generalized Fermat Numbers (GFN). We briefly review the history of the GFN prime search, and describe new implementations of the ‘Genefer’ software (now available as open source) using CUDA and optimised CPU assembler which have underpinned this unprecedented progress. The results of the ongoing search are used to ...
متن کاملVerifying Two Conjectures on Generalized Elite Primes
A prime number p is called b-elite if only finitely many generalized Fermat numbers Fb,n = b 2 + 1 are quadratic residues modulo p. Let p be a prime. Write p − 1 = 2h with r ≥ 0 and h odd. Define the length of the b-Fermat period of p to be the minimal natural number L such that Fb,r+L ≡ Fb,r (mod p). Recently Müller and Reinhart derived three conjectures on b-elite primes, two of them being th...
متن کاملNotes on Generalized Fermat Numbers
There are two different definitions of generalized Fermat numbers (GFN), one of which is more general than the other. In [5], Ribenboim defines a generalized Fermat number as a number of the form Fa,n = a n + 1 with a > 2, while Riesel ([6]) further generalizes, defining it to be a number of the form a n + b n . Both definitions generalize the usual Fermat numbers Fn = 2 n + 1. The only known F...
متن کاملOn Silverman's conjecture for a family of elliptic curves
Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...
متن کاملSimple groups with the same prime graph as $D_n(q)$
Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003