# Finite algebra yielding mostly primes?

#### Loren

Interesting. I guess it is one of the simplest of countless formulas that generate an infinitude of primes.

#### Maschke

Interesting. I guess it is one of the simplest of countless formulas that generate an infinitude of primes.
$f(n) = n$ generates an infinitude of primes. Also an infinitude of composites.

#### romsek

Math Team
I haven't thought it out very deeply but it strikes me that if there was such a function that generated nothing but primes our crypto systems would be next to worthless.

Loren

#### Loren

$f(n) = n$ generates an infinitude of primes. Also an infinitude of composites.
It reminds me of the definition for the null set -- a lot simpler than I had considered before. As it is said, "I'm just not myself."

#### Loren

I haven't thought it out very deeply but it strikes me that if there was such a function that generated nothing but primes our crypto systems would be next to worthless.
"The computability of a problem is closely linked to the existence of an algorithm to solve the problem. " Aren't our current algorithms for determining primes NP, that is, very inefficient over time?