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In additive prime number theory,a classical result of Hua states that,every suffi-ciently large odd number N can be represented as 〓,where 〓 is aninteger and 〓 are primes,which can be regarded as an extension of Goldbach-Vinogradov Theorem.

堆垒素数论中一个经典的结果是华罗庚教授证明的：任一个充分大的奇数N都可以表为N=〓+〓+〓，其中λ是一正整数，p1，p2，p3是素数，这一结果可以看作著名的Goldbach-Vinogradov定理的推广。

An arithmetic progression of primes is a sequence of primes with a common difference between any two successive numbers in the sequence.

在一个等差数列，任意相邻两项的差都是相等的。

Since the problem of GVT with two primes restricted in arithmetic progressionsof the same moduli k is actually the same as the previous problem(2),we consideredthe problem of GVT with exactly one prime in an arithmetic progression.

两个素数取值于相同模的算术级数中的GVT问题实际上和前面的的问题（2）是一样的，于是只需考虑一个素变数在算术级数中取值的奇数Goldbach问题。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

This isn't as easy as it may sound, only 12 Cullen primes and 15 Woodall primes have ever been found, however, we believe that PrimeGrid has sufficient computing power to make this search plausible.

这并不像看起来那么容易，到现在为止也只发现了 12 个 Cullen 质数和 15 个 Woodall 质数。然而，我们相信 PrimeGrid 拥有足以进行这个搜索的计算能力。

The prime is 1,129,757 digits long and enters The Largest Known Primes Database ranked 1st for Woodall primes and 13th overall.

这个质数的十进制表示长度为 1129757 位，被收入了已知大质数数据库，大小在已找到的 Woodall 质数中排第一，在所有已找到的最大质数中排第 13。

It is 712818 digits long and enters The Largest Known Primes Database ( http://primes.utm.edu/primes/) ranked 1st for Woodall primes and 25th overall.

这个质数有 712818 位十进位，是迄今为止发现的最大的 Woodall 质数，也是迄今为止发现的第 25 大的质数。

1 The prime is 606279 digits long and enters The Largest Known Primes Database ( http://primes.utm.edu/primes/) ranked 1st for Woodall primes and 37th overall.

这个质数有 606292 位十进位，是迄今为止发现的最大的 Woodall 质数，也是迄今为止发现的第 37 大的质数。

If the mediated primes were orthographically different from the semantic primes, the mediated priming effect was significantly different from the direct semantic priming effect.

如果中介启动字与语义相关启动字同音但是形异时，得到的语音中介启动与直接的语义启动有显著差异。

The results illustrated that the priming effect from the homophonic primes was equal to the direct semantic effect when phonological primes were orthographically similar to the semantic prime.

实验五的结果发现，当同音中介启动与语义相关启动不但同音而且形似时，语音中介启动效应与直接的语义启动效应差异不显著。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了