100 primes

[MooMoo2]

Congrats to pacionet, who has found the 100th prime!

572393475*2^195000-1

[pacionet]

I am happy
let's go on this way !

[MooMoo2]

We're at 200 primes now

[KEP]

Originally Posted by MooooMoo

We're at 200 primes now

Yeah! ! ! More than 7 bit primes, I'm just wondering if we shouldn't be capeable of hitting the 8th bit of primes, and maybe even more.... sighhh but if we have to find 4000 primes before hitting a twin, or even more, we will definently still have a long way to walk But we can do it of course we can, maybe even within next summer :) And what the ("beeeep") it gives our project plenty of time to sieve the new n to a huge depth

Regards!

[biwema]

At 50 Bit sieving depth (1126T) one can expect one twin every 2184 primes, at 52 Bit every 2100 prime.

Let's hope that we a re not too unlucky.

[amcfarlane]

Originally Posted by biwema

At 50 Bit sieving depth (1126T) one can expect one twin every 2184 primes, at 52 Bit every 2100 prime.

I'm curious as to how this was deduced...

[KEP]

Originally Posted by biwema

At 50 Bit sieving depth (1126T) one can expect one twin every 2184 primes, at 52 Bit every 2100 prime.

Let's hope that we a re not too unlucky.

I'm also currious as to how you came up with these figures. Maybe I doesn't get the sieving, but isn't sieving only removing the non-primes, and leaving the primes+non-sieved prime candidates? If that assumption is correct, then the amount of primes should be the same no matter your sieving depth, and therefor also the amount of primes needed to be found before yielding a twin should be stable. If I'm wrong, then please tell me how the numbers can change...

Regards!

[smh]

Originally Posted by KEP

I'm also currious as to how you came up with these figures. Maybe I doesn't get the sieving, but isn't sieving only removing the non-primes, and leaving the primes+non-sieved prime candidates? If that assumption is correct, then the amount of primes should be the same no matter your sieving depth, and therefor also the amount of primes needed to be found before yielding a twin should be stable. If I'm wrong, then please tell me how the numbers can change...

No, sieving does remove primes!

The sieving is looking for composites of both the +1 and -1 side. If a factor is found for either one, the number is removed from the list. So, the -1 number might well be prime, but that number isn't tested because the +1 number had a small factor.

[KEP]

Originally Posted by smh

No, sieving does remove primes!

The sieving is looking for composites of both the +1 and -1 side. If a factor is found for either one, the number is removed from the list. So, the -1 number might well be prime, but that number isn't tested because the +1 number had a small factor.

OK, that might explain why the amount of "normal" primes found before twin is found, is reduced. Thanks for the reply.

[biwema]

Yes.

You are sieving for twins, therefore the number of twins remains constant, but not the number of normal primes.

Example:
When you sieve up to Sqrt(candidate), every remaining prime is also a twin.

[MooMoo2]

300 primes now

Time to find the first 100 primes: more than 5 months
Time to find the second 100 primes: about 2 and a half months
Time to find the third 100 primes: less than 3 weeks :surprised