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Are there prime numbers over 400?

Updated: 8/17/2019
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14y ago

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Yes, in fact, there is no last Prime number - the set of prime numbers is infinite. The proof was already known 2000 years ago:

If you assume that there is a last prime number, multiply all prime numbers up to that "last prime number". Then add one. The result is either a prime number itself, or it is composed of factors, none of which is one of the prime numbers you multiplied (because of the added 1). Thus, the original assumption (that there is a last prime number) has to be false.

Example: The first 3 prime numbers are 2, 3, 5. If you multiply them, you get 30. Add one to the result, and you get 31. This number isn't divisible by 2, by 3, nor by 5. It happens to be a prime, but this isn't always so.

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14y ago
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Q: Are there prime numbers over 400?
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