Table of prime numbers from 1 to 1000

A prime number is a natural number that is divisible without a remainder only by 1 and by itself. For example, the numbers 2, 3, 5, 7, 11 are prime. Numbers that have other divisors are called composite (for example, 4, 6, 8, 9).

On this page is the complete table of prime numbers from 1 to 1000, as well as the definition, properties, and examples of use.

What is a prime number

A prime number is a natural number greater than 1 that has exactly two divisors: 1 and itself.

Examples of prime numbers: 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, etc.

Important:

• The number 1 is neither prime nor composite — it has only one divisor (1).
• The number 2 is the only even prime number. All other prime numbers are odd.
• There are infinitely many prime numbers (Euclid's theorem).

How to find prime numbers: sieve of Eratosthenes

The simplest way to find all prime numbers up to a given number is the sieve of Eratosthenes. Algorithm:

1. Write down all numbers from 2 to N.
2. The first number (2) is prime. Cross out all multiples of 2 (4, 6, 8, 10…).
3. The next uncrossed number (3) is prime. Cross out all multiples of 3 (6, 9, 12…).
4. The next uncrossed number (5) is prime. Cross out all multiples of 5.
5. Continue until you reach a number whose square is greater than N.
6. All remaining uncrossed numbers are prime.

Table of prime numbers from 1 to 1000

Below is the complete table of prime numbers up to 1000. Numbers are grouped by hundreds for ease of search.

Properties of prime numbers

• Infinity: There are infinitely many prime numbers (proven by Euclid).
• The only even prime number: The number 2 is the only even prime number.
• Fundamental theorem of arithmetic: Any natural number greater than 1 can be uniquely decomposed into prime factors.
• Twin primes: Pairs of prime numbers whose difference is 2 (for example, 3 and 5, 11 and 13, 17 and 19).
• Distribution: As numbers grow, prime numbers occur less frequently (prime number theorem).

Examples of using the table of prime numbers

Example 1. Check whether 97 is prime

We look for the number 97 in the table. It is in the list — therefore, 97 is a prime number.

Answer: 97 is a prime number.

Example 2. Decompose the number 84 into prime factors

Use the table of prime numbers:

84 = 2 × 42 = 2 × 2 × 21 = 2 × 2 × 3 × 7

Answer: 84 = 2² × 3 × 7.

Example 3. Find all prime numbers from 50 to 70

From the table: 53, 59, 61, 67.

Answer: 53, 59, 61, 67.

Compiled by: Alexey Pavlov, mathematics teacher.
Source: classic mathematical reference books, sieve of Eratosthenes.
Last updated: 11.10.2026.