Twin prime search?

[pacionet]

...but it will lead to confusion if we do decide (later) to test for primes of k*2^195001-1. I'm definitely not planning to move to another n any time soon, but there is a small chance that the situation may change.

In my opinion we must check at least until 5G before switching another exponent. Anyway we are still too few searchers ! (5 ? 6 ? 7 ?)

Please join us !!!

[MooMoo2]

Originally Posted by pacionet

In my opinion we must check at least until 5G before switching another exponent. Anyway we are still too few searchers ! (5 ? 6 ? 7 ?)

Please join us !!!

I second your opinion to wait until at least 5G. After that, if most people want to change n's and check even k's as well as odd k's, I'm fine with it. I just don't like the idea of choosing a new n and wasting 100T worth of sieving.

I have no objection to distributed sieving. If you're interested in participating, post in the "sieving discussion thread". The problem will be getting a factor verification system that will automatically make changes to the list of k's to test.

[Numbers]

I trust an interested non-participant can make a point.

It is not a question of whether k should be odd or even.

Let a, b, be twin prime of the form 6q + r where r = (1, 5) (a < b)

Then a == 5(mod 6) and b == 1(mod 6)

and a = 6q + 5, b = 6(q + 1) + 1

so that a + b = 12q + 12 and a + 1 = 6q + 6

Therefore, a + 1 == 0(mod 6)

Now, when searching for numbers d of the form k(2^n)

where it is hoped that d +- 1 are twin prime,

then d needs to be == 0(mod 6), and therefore k == 0(mod 3).

I suggest that you will speed up your search considerably
if you adopt this approach.

[John Renze]

Numbers, this was the very first step taken by the sieve. In fact, unless I am reading your comment wrong, "sieving" is simply generalizing this to primes > 3. For an odd prime p, there are always exactly two congruence classes which can be eliminated.

[Numbers]

John,
Well I will be the first to admit that I may have misunderstood what you were doing.

From this post...

Originally Posted by MooooMoo

1.) I used the "twin search" feature in NewPGen to sieve out factors less than, say 10 trillion. For those numbers, k*2^n +1 and k*2^n-1 doesn't have a factor less than 10 trillion.

I assumed you were sieving values of k(2^n)- 1.

Then, from this post...

Originally Posted by MooooMoo

2.) We'll put those numbers in PRP, which will search for primes of k*2^n+1 only.

I assumed that if you find a prime then you use PRP to check + 1.

That is what you are doing, right?

Well, from this post...

Originally Posted by MooooMoo

As for now, the n is 195,000, with k searched for all values below 100,000.

emphasis added by me.

and this post...

Originally Posted by MooooMoo

Also, there are plenty of odd k's to test, and a k around 20M takes the same time to test as a k around 200M. So even if we decided to test even k's, there would not be a speed improvement.

It would appear that MooooMoo at least is not aware that the choice of k is not about whether k is odd or even.

The point of my post was that you can eliminate two thirds of your candidates before you start sieving by simply making sure that k is divisible by 3.

If k is not divisible by 3 then k(2^n)+- 1 will not be twin prime.

If you, or your team, were not aware of this then why were they discussing whether k should be odd or even? It doesn't matter whether it is odd or even, what matters is that k MUST be divisible by 3.

[lsoule]

Originally Posted by MooooMoo
As for now, the n is 195,000, with k searched for all values below 100,000.

That just means that all values of k<100,000 were either sieved out or LLR'd.
The sieving step takes care of the divisible by 3 problem pretty quickly
and efficiently. None of the available ranges have an k's that are not
divisible by 3.

[MooMoo2]

Originally Posted by Numbers

I assumed that if you find a prime then you use PRP to check + 1.

That is what you are doing, right?

I did write:

2.) We'll put those numbers in PRP, which will search for primes of k*2^n+1 only

However, that post was from 2 months ago. At that time, I wasn't sure on whether to check +1 or -1 first. Later, I decided on -1 because it was slightly faster:

168367377*2^195000-1 is prime! Time : 95.454 sec.
168367377*2^195000+1 is not prime. Proth RES64: 2A409B23B3D7987E Time: 95.728 sec.

186002877*2^195000-1 is prime! Time : 104.031 sec.
186002877*2^195000+1 is not prime. Proth RES64: 29FD50C0848E4FEE Time: 104.398 sec.

I simply forgot to edit the post from 2+ months ago.

[pacionet]

I tried to make range reservation automatic.
Please try the dynamic website here:

http://www.twinprimesearch.org/TPS-DIN/index.htm

Try to register (you should receive an email for confirmation, but for some email acconunt there can be some problems, in such case I'll confirm your registration manually).

Then try to reserve a range (it is only a test , the reservation is not valid, do the valid reservations on the forum as usual), try to set the range as "completed" with the number of primes found.

When you reserve a range the site checks that the SAME range is not ALREADY reserved by somebody else, but if the range differs slightly it is quite difficult to avoid the reservation.

So always check the status page.

[Skligmund]

So at what point does this search start 'making the books'? Oviously when a Twin Prime is found, but what other milestones (if any) do we have to look foward to?

[MooMoo2]

For psychological, feel good milestones, you could use the number of primes found as milestones. For every 100 primes found, there'll be something to be happy about.

Other than that, finishing 25G and finding a twin prime are about the only concrete milestones. Finishing 25G means we'll move to a new n, while finding a twin gets us a world record. As for "getting in the books", the only way to do so is when we get that twin. Even if we find a million non-twin primes, no list of records will recognize the project for that achievement.

This situation will likely change once we move to the next n, since finding non-twin primes for that n will still get those primes into the list of the top 5,000 primes.

[Skligmund]

Okay, thats what I figured. Thanks for the reply, I hope we find that twin prime soon!