搜索结果: 1-12 共查到“数论 primes”相关记录12条 . 查询时间(0.109 秒)
In this paper we bring into attention an old subject in number theory. Fermat showed that a prime can be written as a sum of two squares if and only if it is a multiple of four plus one and the decomp...
A Diophantine problem with a prime and three squares of primes
Goldbach-type theorems Hardy-Littlewood method diophantine inequalities
2012/6/14
We prove that if $\lambda_1$, $\lambda_2$, $\lambda_3$ and $\lambda_4$ are non-zero real numbers, not all of the same sign, $\lambda_1 / \lambda_2$ is irrational, and $\varpi$ is any real number then,...
In the present work we investigate the largest possible gaps between consecutive numbers which can be written as the difference of two primes. The best known upper bounds are the same as those concern...
Mersenne Primes in Real Quadratic Fields
Mersenne Primes Real Quadratic Fields Number Theory
2012/5/24
The concept of Mersenne primes is studied in real quadratic fields of class number 1. Computational results are given. The field $Q(\sqrt{2})$ is studied in detail with a focus on representing Mersenn...
Every prime larger than 3 is arithmetic mean of other two primes
prime distribution of primes arithmetic progression Goldbach conjecture
2011/9/21
In this paper a new stronger proposition has been advanced and shown, that is, every prime larger than 3 is arithmetic mean of other two primes, and other important propositions that there are infinit...
The irregular distribution of primes up to 300,000 in the sequence of odd numbers
prime distribution of primes
2011/9/19
In this paper we listed a sequence of odd numbers up to 300,000 by a computer calculating and it could be find that the density of prime numbers is decreased as odd number increases and that there exi...
There are infinitely many primes of the form a^2 +1
primes in polynomials sieve method limit of sequences Godel completeness theorem Ross-Littwood paradoxset
2011/9/18
In this paper we founded a formal system of second order arithmetic $\langle P(N), +, \times, 0, 1, \in \rangle$ by extending the operations $+, \times$ on natural numbers to the operations on finite ...
Abstract: We consider the second of Mullin's sequences of prime numbers related to Euclid's proof that there are infinitely many primes. We show in particular that it omits infinitely many primes, con...
The Skewes number for twin primes: counting sign changes of $π_2(x)-C_2 \Li_2(x)$
Primes twins Skewes number Number Theory
2011/9/6
Abstract: The results of the computer investigation of the sign changes of the difference between the number of twin primes $\pi_2(x)$ and the Hardy--Littlewood conjecture $C_2\Li_2(x)$ are reported. ...
On Hecke eigenvalues at primes of the form $[g(n)]$
Hecke eigenvalues, Piatetski-Shapiro primes
2011/8/30
Abstract: In this paper, we study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form $[g(n)]$.
Let a and b be positive integers and let p be an odd prime such that p =ax2+by2 for some integers x and y.
On the symmetry of primes
symmetry primes
2010/12/15
We prove a kind of “almost all symmetry” result for the primes, i.e. we give non-trivial bounds for the “symmetry integral”, say I(N, h), of the von Mangoldt function (n) (:= log p for prime-powers ...