What is a prime number?
A prime is a whole number greater than 1 whose only divisors are 1 and itself: 2, 3, 5, 7, 11, 13, and onward forever, a fact Euclid proved around 300 BC with an argument still taught today. Two footnotes settle the classic quibbles: 2 is the only even prime, and 1 is not prime, by definition, because the fundamental theorem of arithmetic, every number factors into primes exactly one way, collapses if 1 gets membership.
That theorem is why primes matter: they are the atoms of arithmetic, the indivisible pieces every other whole number is built from. 60 is 2 times 2 times 3 times 5, and no other combination.
The practical punchline is in your pocket: modern encryption, including the systems securing your credit card and messages, rests on the fact that multiplying two enormous primes is easy while factoring the result back apart is computationally brutal. The largest known primes now run to tens of millions of digits, found by distributed volunteer computing.
A whole number greater than 1 divisible only by 1 and itself: 2, 3, 5, 7, 11. They are the atoms of arithmetic, there are infinitely many, and your credit card security runs on them.
- Euclid, Elements, Book IX
- NIST cryptographic standards
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https://frequentlyaskedquestions.us/q/what-is-a-prime-number/Everybody Asks. (2026, July 28). What is a prime number? https://frequentlyaskedquestions.us/q/what-is-a-prime-number/“What is a prime number?” Everybody Asks, 28 July 2026, https://frequentlyaskedquestions.us/q/what-is-a-prime-number/.“What is a prime number?” Everybody Asks. Last modified July 28, 2026. https://frequentlyaskedquestions.us/q/what-is-a-prime-number/.This page summarizes the primary sources listed above. For academic or encyclopedic work, cite those primary sources directly wherever possible.