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Every whole number above one breaks into primes in exactly one way, order aside.

Mathematics Facts, sourced to Wolfram MathWorld.

What it means

This is why one is not treated as a prime. If it were, you could pad any factorization with as many ones as you liked and uniqueness would fail. The theorem is the reason primes are called the building blocks of arithmetic, and the fact that factoring a large number is hard while multiplying is easy is what most public key cryptography rests on.

The claim comes from Wolfram MathWorld, and the page it comes from was read on 2026-08-27 to confirm it still says this.

This is not the kind of claim that goes out of date, which is why it was set as a puzzle rather than a fact with a shelf life.

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