Number Theory 10 min read

Prime Numbers List (1 to 1000) & Primality Testing Rules

Complete list of prime numbers from 1 to 1000. Learn fundamental primality rules, trial division methods, and the Sieve of Eratosthenes.

Table of Contents

What Is a Prime Number?

A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. The number 2 is the only even prime number.

First 25 Prime Numbers (Up to 100)

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Fast Primality Testing Rules

  • Ending Digit Rule: Any number ending in 0, 2, 4, 5, 6, 8 (except 2 and 5) is composite.
  • Sum of Digits Rule: If the sum of a number's digits is divisible by 3, the number itself is divisible by 3.
  • Trial Division: To test if N is prime, test division only up to √N.
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Reviewed by Applied Math Specialists • Editorial Policy
Updated: August 11, 2026

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