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

If the number is odd, add the smallest prime number not yet added.

From New York Times • May 21, 2023

Two is my favorite number, so it’s definitely my favorite prime number.

From Scientific American • Nov. 22, 2022

“They’ll give us an idea of what you’re in for. For instance: What is the largest two-digit prime number less than a hundred?”

From "The Smartest Kid in the Universe" by Chris Grabenstein