How many prime numbers have we actually solved

[evolvehuman]

how many prime numbers have we actually solved,,, how can we say that there is no end to prime when we can't even count that high, i think sooner or later all numbers higher than primegod would be not prime

 

[CRGreathouse]

how can we say that there is no end to prime when we can't even count that high, i think sooner or later all numbers higher than primegod would be not prime

The usual way of proing that there are infinitely many primes is Euclid's proof: if the only primes were (p1, p2, ..., pk) then P = p1 * p2 * ... * pk + 1 cannot be divisible by any of p1, ..., pk, and so P is divisible by a prime other than p1, ..., pk.

One technique you might like: the Fermat numbers 2^(2^n) + 1 are pairwise relatively prime, so each contains at least one prime not previously occurring as a Fermat number divisor.

 

[evolvehuman]

i still believe the math is going to egg

 

[fss]

i still believe the math is going to egg

Hmm... I don't think so. At least I'm not going to hold my breath.

 

[evolvehuman]

further prime should have a different formula or all prime won't be contained

 

[evolvehuman]

unless we are just trying to find any prime then there will be holes in the grid

 

[CRGreathouse]

further prime should have a different formula or all prime won't be contained

Do you mean that the Euclid-Mullin sequence, Sloane's A000945, doesn't contain all primes?

That problem is still open. If you think you have a proof, try to write it up.

 

[evolvehuman]

just being dumb prove 139 is prime by the e-m sequence for me please, ...
a(1) = 2, a(n+1) _{k=1..n} a(k) + 1

 

[HallsofIvy]

This is ridiculous. I am closing the thread.