prime number

American  

noun

Mathematics.

1. a positive integer that is not divisible without remainder by any integer except itself and 1, with 1 often excluded.

   The integers 2, 3, 5, and 7 are prime numbers.

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prime number British  

noun

1. Sometimes shortened to: prime.  an integer that cannot be factorized into other integers but is only divisible by itself or 1, such as 2, 3, 5, 7, and 11 Compare composite number

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prime number Scientific  

1. A positive integer greater than 1 that can only be divided by itself and 1 without leaving a remainder. Examples of prime numbers are 7, 23, and 67.

2. Compare composite number

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prime number Cultural  

1. A number that cannot be divided evenly by any other number except itself and the number one; 1, 3, 5, 7, and 11 are prime numbers.

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Etymology

Origin of prime number

First recorded in 1585–95

Example Sentences

Six is a perfect number, and seven is a prime number, but only a glutton for punishment would put them together in front of a bunch of 13-year-olds.

From The Wall Street Journal • Oct. 14, 2025

“It’s like an entire alien species living underneath our feet and then some prime number years they come out to say hello.”

From Seattle Times • Apr. 1, 2024

After all, it is neither a prime number nor a power of 2 nor a square number.

From Scientific American • Mar. 3, 2023

Sixty-one is a prime number, just as the Slate News Quiz is a prime example of good quizzing fun.

From Slate • Oct. 7, 2022

I know all the countries of the world and their capital cities and every prime number up to 7,057.

From "The Curious Incident of the Dog in the Night-Time" by Mark Haddon