Solved cryptogram
The prime numbers never run out. Euclid proved it with an argument you can follow in a minute.
Mathematics Facts, sourced to Wolfram MathWorld.
What it means
Suppose you had a complete list of primes. Multiply them all together and add one. The result leaves a remainder of one when divided by every prime on your list, so either it is prime itself or it has a prime factor you missed. Either way the list was incomplete. The proof is over two thousand years old and has never needed patching.
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This is not the kind of claim that goes out of date, which is why it was set as a puzzle rather than a fact with a shelf life.
Solve it yourself
This fact is a cryptogram here: 75 letters over 21 different ones, graded hard.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultyhard
- Length75 letters, 21 of them different
Nearby in the collection
The facts either side of this one.
- Wolfram MathWorldmedium, 76 letters
- Wolfram MathWorldmedium, 77 letters
- Wolfram MathWorldmedium, 72 letters
- Wolfram MathWorldhard, 65 letters
About as hard as this one
Scored closest to it by the model behind our guide to solving cryptograms.
- Wolfram MathWorldmedium, 81 letters
- Wolfram MathWorldhard, 79 letters
- Wolfram MathWorldmedium, 79 letters
- Wolfram MathWorldmedium, 75 letters