Scarblac
01-10-2003, 10:02 AM
I've been wondering if we have a chance to ever find the biggest prime at that moment. Will GIMPS or some other project always be in front?
Assume equal computing power for a moment (we're not there yet I suppose, but who knows). Our numbers are of the form k2^n+1; we sieve a lot too. GIMPS are in front and search primes of the form 2^n-1, in terms of digits that's basically the same, I'm assuming they sieve as much as we do, at least.
We also search for several factors k at the same time.
As far as I remember (all this theory is vague in my head), Mersenne primes are easier to prove than Proth primes.
If we're lucky, there won't be another Mersenne prime for a long time, so we could pass them and find a bigger prime than they have, by pure luck.
Other than being lucky, we don't have much chance of passing them, right? How much more computing power would we need, relative to GIMPS?
Are there other projects who might find bigger primes even faster? Am I forgetting anything that influences this?
Assume equal computing power for a moment (we're not there yet I suppose, but who knows). Our numbers are of the form k2^n+1; we sieve a lot too. GIMPS are in front and search primes of the form 2^n-1, in terms of digits that's basically the same, I'm assuming they sieve as much as we do, at least.
We also search for several factors k at the same time.
As far as I remember (all this theory is vague in my head), Mersenne primes are easier to prove than Proth primes.
If we're lucky, there won't be another Mersenne prime for a long time, so we could pass them and find a bigger prime than they have, by pure luck.
Other than being lucky, we don't have much chance of passing them, right? How much more computing power would we need, relative to GIMPS?
Are there other projects who might find bigger primes even faster? Am I forgetting anything that influences this?