完全数

当前已发现的最大的素数及完全数

What are the largest prime number and perfect number found at present

完全数、相亲数以及孤立数一直是数论研究的一个重要课题。

Perfect number , amicable number and anti-sociable numbers are important topics in number theory .

分类器确定正整数为过剩数（abundant）、完全数（perfect）或亏数（deficient）。

The classifier determines if a positive integer is abundant , perfect , or deficient .

关于奇完全数的Euler因子及其次数

On the Euler 's factor and its order of odd perfect numbers

接下来，我将把所有因子加起来，并最终编写上面所示的公式的Java版本以确定是否为完全数。

Next , I sum all the factors and finally write the Java version of the formula shown above to determine perfection .

奇完全数的Euler因子

The euler 's factors of odd perfect numbers

在Wikipedia上查找到前几个完全数之后，我可以编写一个测试，它检查实际上是否可以找到完全数。

After checking with Wikipedia to find the first few perfect numbers , I can write a test that verifies that I can in fact find perfect numbers .

对于不熟悉数学知识的人，此概念可追溯到Euclid之前（他完成了导出完全数的早期验证之一）。

For those of you not up on your math trivia , the concept goes back to before Euclid ( who did one of the early proofs deriving perfect numbers ) .

现在我有了后测试版本的完全数查找程序。

Now I have a test-after version of the perfect-number finder .

关于奇完全数的存在问题完全数简介

Essential Condition of the Odd Complete Number PROBLEM ABOUT PERFECT NUMBER

形如4p~aq~b的e-完全数

Powerful e - perfect numbers with form 4p ~ aq ~ b

为此，我选择了完全数。

To that end , I 've chosen perfect numbers .

我需要确定某个数字是不是完全数。

I need to determine if a number is perfect .

这就是要处理的问题域：创建一个完全数查找程序。

That 's the problem domain to tackle : create a perfect-number finder .

奇完全数的判定及素因数个数的估算

Decision of Odd Perfect Number and Number of Prime Factors of Odd Perfect Numbers

在开始研究完全数问题时，我把它分解为几个子任务。

When starting this exploration of the problem , I decomposed it into several subtasks .

酉完全数的一个结果

The Result of Unitary Perfect Numbers

到目前为止，我以处理完全数为背景讨论了紧急设计。

Thus far , I 've discussed emergent design in the context of the perfect-numbers problem .

这段代码报告我的完全数算法工作正常，但是它非常慢。

This code reports that my perfect-number algorithm works correctly , but it 's very slow .

关于酉完全数

On the Unitary Perfect Number

完全数简介

Problem about perfect number

这段代码正确地报告了完全数，但是由于反向测试的原因，代码运行得非常慢，因为我需要检查大量数字。

This code correctly reports perfect numbers , but it runs very slowly for the negative test because I 'm checking so many numbers .

人类在研究与寻找完全数时得到结论：偶完全数与梅森素数是一一对应关系。

When researching and looking for the perfect numbers , man found the conclusion about correspondence between the even perfect numbers and the Mersenne primes .

我试图解决的问题是确保我的数字分类器不会将非完全数识别为完全数。

What problem am I trying to solve ? I need to make sure that my number classifier doesn 't identify an imperfect number as perfect .

更规则的完全数定义是因子（不包括该数字本身）之和等于该数字的数字。

A more algorithmic definition for a perfect number is a number where the sum of the factors ( excluding the number itself ) equals the number .

本文主要介绍偶完全数的性质并加以证明，同时也介绍与偶完全数有关的概念和结论。

In this paper , we give a some of concept relating to even perfect number , then give the property of eren perfect number and prove it .

本文给出素数和完全数的定义，还给出了当前世界上最大的素数和完全数。

In this paper , the definitions of prime number and perfect number are introduced , and the largest of them having been found at present in the world are also described .

在下一期文章中，我将继续讨论完全数问题，演示在执行测试时形成的各种设计的更多示例。

In the next installment , I 'll continue with the perfect numbers problem , illustrating more examples of the kinds of design that can emerge if you get out of the way of your tests .

本文对H公式统一了不同的完全相关数对的规律，H公式与异常级数和素数公式之间的联系，H公式与哈代-季特伍德公式的关系作了一定的分析研究与探讨。

This paper has unified the regularity of the different perfect relative numbers , and finds the relationship between the H-formulary and queer sequence > prime number formulary and studied the relations between the H-formulary and Little wood formulary .

对于每个整数，都是完全平方数。

For all integers , is a perfect square .