prime number

素数

Number Theory · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: prime

Translation evidence: Literature usage

Meaning in context

A positive integer $p>1$ whose only positive divisors are $1$ and $p$.

仅有 $1$ 和自身两个正因数的大于 $1$ 的正整数。

Example

$29$ is prime; testing $2,3,5$ suffices.

Usage and distinctions

One is excluded, and primality here concerns positive integers; prime elements in other rings have a different ambient definition.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Thomas W. Judson — Abstract Algebra: Theory and ApplicationsSubsection 2.2.2, opening prime definition · Checked 2026-10-14

Translation sources

1. 新乡学院数学与统计学院 — 初等数论课程教学大纲第一章 整数的可除性，基本概念段落 素数，PDF page 2 (zero-based index 1); name evidence only · Checked 2026-10-15

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