Much as every integer can be broken down into a product of prime Numbers, the symmetries of any object can be constructed from a collection of basic building blocks known as simple groups.

正如每个整数都可用一些质数的积表示，任一对象的对称都可由所谓简单群的基本构件集合构造出来。

You could also write code that USES a positive integer's factors to determine if it is a prime number (defined as an integer greater than 1 whose only factors are 1 and the number itself).

您还可以编写代码，用一个正整数的因子来确定它是否为素数(定义为大于1的整数，该数字仅有的因子为1和本身)。

A prime number is an integer greater than or equal to 2 that has exactly two distinct natural number divisors, 1 and itself.

素数是指大于等于2且只有两个不同约数的整数：1和它自己。

The integer 1 is divisible only by itself; it is not a prime.

整数1只能被它本身整除，所以不是素数。

Diophantine equation; prime; integer solution; Legendre symbol; congruence.

丢番图方程；素数；整数解；勒让德符号；同余。

It is used to find prime, prime twins, prime three folds or different ways of "1 + 1" to an even integer in some interval.

应用此法可直接寻找懦个区间内的素数、孪生素数、三生素数及任一偶数的“1 + 1”型式。

This paper utilizes the Reciprocal Law Two Times to prove that the rational number of a kind of form is not the integer, and proves that the number of another kind of prime is limitless.

利用二次互反定律证明了某类形式的有理数不是整数，并且证明了某类形式的素数的个数是无限的。

Every positive integer greater than 1 can be expressed as the product of prime Numbers.

每个大于1的正整数都能表示为素数的乘积。