Is it true that any rule regarding prime numbers eventually fails?

1. Oct 27, 2013

goldust

Other than the fact that prime numbers are infinite?

2. Oct 27, 2013

Staff: Mentor

By rule, you mean one that predicts primes then yes they all fail.

3. Oct 27, 2013

goldust

Not just prediction of prime numbers, but any regularity that humans can comprehend. The regularity must be directly operated on primes rather than on another set of numbers, such as the statement that every even number is the sum of two primes, or every even number is the sum of a prime and a semi prime. Also, the regularity can't be probabilistic as in the Prime Number Theorem.

Last edited: Oct 27, 2013
4. Oct 27, 2013

eigenperson

No, it is not true. How could it be?

This page has many examples of formulas that generate all the primes (and only the primes).

5. Oct 27, 2013

goldust

Do any of them take prime numbers as inputs?

6. Oct 27, 2013

eigenperson

I don't quite understand your question -- are you asking for something like a formula that takes a number as input, and returns 1 if it is prime and 0 if it is non-prime?

If so, take a look at Wilson's Theorem (or at the first formula on the page I just linked to).

7. Oct 27, 2013

goldust

Wilson's formula is very interesting. Thanks for the info.

Last edited: Oct 27, 2013