搜索结果: 1-15 共查到“数论 prime”相关记录20条 . 查询时间(0.223 秒)
商洛学院数学与计算机应用学院初等数论课件Chapter 1 Prime Numbers.
Strong pseudoprimes to the first 9 prime bases
Strong Pseudoprimes Chinese Remainder Theorem
2012/7/9
Define $\psi_m$ to be the smallest strong pseudoprime to the first $m$ prime bases. The exact value of $\psi_m$ is known for $1\le m \le 8$. Z. Zhang have found a 19-decimal-digit number $Q_{11}=3825\...
A Diophantine problem with prime variables
Diophantine problems with prime variables Number Theory
2012/6/14
We study the distribution of the values of the form $\lambda_1 p_1 + \lambda_2 p_2 + \lambda_3 p_3^k$, where $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real number not all of the same sign,...
L^2-norms of exponential sums over prime powers
Primes in short intervals Diophantine problems with primes Number Theory
2012/6/14
We study a suitable mean-square average of primes in short intervals, generalizing Saffari-Vaughan's result. We then apply it to a ternary Diophantine problem with prime variables.
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,...
The variance of the number of prime polynomials in short intervals and in residue classes
variance the number of prime polynomials short intervals residue classes Number Theory
2012/4/23
We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial i...
In this paper we extend the proof of the twin prime conjecture to prove the Sophie Germain prime conjecture and to attack the Cunningham chain. We show also that there are infinitely many composites i...
There always exists at least one prime between x and x+x^{1/2} when x is sufficiently large
Pprime distribution of primes
2011/9/21
In this paper one has shown that there always exists at least one pseudo prime number between x and x+x^{1/2} when x is sufficiently large for a pseudo sequence of odd numbers, so it also is true that...
There always exists at least one prime between x and x+log^2(x) when x> =8
Prime distribution of primes
2011/9/21
In this paper one has shown that there always exists at least one pseudo prime number between x and x+log^2(x), so it also is true that there always exists at least one real prime number for the real ...
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...
Every even number is equal to the difference of two prime number
sieve method two-dimension sieve method even number
2011/9/21
This paper have proved a conjecture about that every even number is equal to the difference of two prime numbers by using a two-dimension sieve method of using odd composites to the difference formula...
The distribution of pseudo prime numbers up to 300,000 in pseudo sequence of odd numbers
prime pseudo prime distribution of pseudo primes
2011/9/19
In this paper a pseudo sequence of odd numbers had been advanced, and the number of pseudo prime numbers in it are largely less than the real prime numbers in the real sequence of odd numbers. This ps...
The proofs of twin prime conjecture and weaker Polignac's conjecture
prime distribution of primes twin primes Polignac's conjecture Goldbach-type problem
2011/9/18
This paper advanced a new method of appointedly covering prime circles with level colors of black degree, and showed twin prime conjecture and weaker Polignac's conjecture to be true with the proof by...
A binomial identity on the least prime factor of an integer
binomial identity least prime factor of an integer Number Theory
2011/9/22
Abstract: An identity for binomial symbols modulo an odd positive integer $n$ relating to the least prime factor of $n$ is proved. The identity is discussed within the context of Pell conics.
Average estimate for additive energy in prime field
Average estimate additive energy prime field Number Theory
2011/9/19
Abstract: Assume that $A\subseteq \Fp, B\subseteq \Fp^{*}$, $\1/4\leqslant\frac{|B|}{|A|},$ $|A|=p^{\alpha}, |B|=p^{\beta}$. We will prove that for $p\geqslant p_0(\beta)$ one has $$\sum_{b\in B}E_{+}...