Project FAQ
 

Q: What is a twin prime?

A: Twin primes are two primes separated by 2. For example, the following are twin primes:

3 and 5
11 and 13
10963863*2^3400 -1 and 10963863*2^3400 +1

Q: What twins are we searching for?

A: We're looking for primes of the form k*2^195000 -1 and k*2^195000 +1.

Q: Will we be double checking any ranges?

A: No. We're trying to find ONE twin prime for n=195000, not ALL of the twin primes for n.

Q: Will we always stick to n=195000?

A: Yes, until we find a twin prime.

Q: What's so special about n=195000?

A: It's an arbitary value, but it's big enough to get a new world record.

Q: What happens after we find a twin?

A: We'll vote on a new n to select.

Q: What is a "K", "M", and "G"?

A: These are SI prefixes. K=1000 M=1,000,000 G=1,000,000,000
The American billion and the European billion are two different numbers, so use the SI prefixes.

Q: What's going on with the sieving? Who's doing it, and why are my posts about sieving deleted?

A: Currently, gribozavr is sieving 100M-25G. There is no distributed sieving yet, and all posts about sieving have been moved to the "sieving discussion thread."

Q: Where do I post my range reservations? "Range reservations thread", or "Pre sieved range reservations thread?"

A: "Range reservations thread" is for ranges below 100M. If you've completed ranges below 100M, post there. If not, post in the "Pre sieved range reservations thread."

Q: What are the limits of LLR?

A: LLR can handle all k values up to 999G.

Q: When will we find a twin?

A: We're expected to find a twin before 20G. For a more detailed analysis:

Probability of finding a twin in a range:
my calculations of n=195000 give...
range
k=5 G chance of finding a twin: 31%
k=10 G chance of finding a twin: 52%
k=20 G chance of finding a twin: 77%
k=25 G chance of finding a twin: 84%
k=30 G chance of finding a twin: 89%
k=40 G chance of finding a twin: 95%
k=50 G chance of finding a twin: 97.5%

Q: How long does a range take to complete?

A: For most users, a range of 1M takes a day to complete, if you leave your computer on 20-24 hours a day.

Q: What are the pros and cons of this project?

A: The bad news is that each candidate you test has about a 1 in 8,000,000 chance of being a twin. This is about the same chance as finding a Mersenne prime by double checking one candidate, and there is no prize money if you find one.

The good news is that one candidate takes less than 2 minutes to test on a fast computer (P4, >2.8 GHz). If you have one fast computer and leave it on close to 24 hours a day, the chance of finding a twin on any given day is 1 in 10,000. Also, if you do find a twin, it'll be a world record.

Q: If we do find a twin, who gets the credit?

A: The person who finds the twin prime in his/her range will be the discoverer, and he/she will share the credit with myself and these people:

- person who completed the most ranges, in M
- person who found the most (non-twin) primes. If this is the same person as the person who completed the most ranges, the person who completed the second greatest amount of ranges (in M) will get the credit.
- anyone who can give LLR or NewPGen a 5% or more speed increase
- If the twin prime is within 100M - 5000M, gribozavr will also get some credit, since he/she's the siever of it. If the prime is above 5000M, the person who sieves the most (in trillion) gets the credit, assuming distributed sieving is available then.

This means that as many as 6 people could end up sharing the credit, which is fine. After all, this project cannot be completed by one or two people alone

Some suggestions.
 

[QUOTE=MooooMoo]
Q: What's so special about n=195000?

A: It's an arbitary value, but it's big enough to get a new world record.

- anyone who can give LLR or NewPGen a 5% or more speed increase
[/QUOTE]


I think we are working on the wrong n. If you choose 2^n instead of 195000, the sieve in theory should be several times faster.

Since computing 2^2^n requires less work than computing 2^195000.

Also, you should remove all perfect squares, cubes, fifth power and 13th power since the -1 side can never be prime for 195000. Newpgen does not remove this.

Hope this make the project faster by atleast 5%.:showoff:

PS: If you do not want to go to a larger n, 196608 will be the best choice. It is about 5% slower to sieve than 262144.
So 262144 is the fastest, 196608 is the second fastest.

[QUOTE=Citrix]I think we are working on the wrong n. If you choose 2^n instead of 195000, the sieve in theory should be several times faster.

Since computing 2^2^n requires less work than computing 2^195000.

Also, you should remove all perfect squares, cubes, fifth power and 13th power since the -1 side can never be prime for 195000. Newpgen does not remove this.

Hope this make the project faster by atleast 5%.:showoff:

PS: If you do not want to go to a larger n, 196608 will be the best choice. It is about 5% slower to sieve than 262144.
So 262144 is the fastest, 196608 is the second fastest.[/QUOTE]
I don't want to switch n's before we find a twin for n=195000. The reason for this is that we've already sieved up to 100T for that n. If we switch, we'll have to start sieving all over from 0.

I'm not too good in programming, but I'd appreciate it if you or anyone else could make a program that removes all perfect squares, cubes, 5th power, and 13th power for the k's. If there is an improvement, I'll tell gribozavr to eliminate those k's from the sieve files.

What will really help sieving (I think) is a native 64-bit sieving program that will take advantage of 64-bit multiplication. I've got an Athlon64, it is currently factoring for 100mdpp, but it can help to sieve too :smile:
I haven't seen such a program yet (or maybe I didn't look in the proper place though).

[QUOTE=MooooMoo]

I'm not too good in programming, but I'd appreciate it if you or anyone else could make a program that removes all perfect squares, cubes, 5th power, and 13th power for the k's. If there is an improvement, I'll tell gribozavr to eliminate those k's from the sieve files.[/QUOTE]

you could write a program to generate all sqaures, cubes, ... and then match if any are left in the sieved file. If gribozavr needs I could write it. Let me know.
We still need to sieve alot, a faster n might save time even though we have already sieved to 100T. But it is up to you, since it is your project.

@gribozavr. Ask greenbank, he might be able to write a fast binary.

One more thing. I would recommend to all users that we work on +1 numbers than -1. We might find a factor of fermat number by doing so, which will be an added bonus to the twin prime.

[QUOTE=Citrix]you could write a program to generate all sqaures, cubes, ... and then match if any are left in the sieved file. If gribozavr needs I could write it. Let me know.
We still need to sieve alot, a faster n might save time even though we have already sieved to 100T. But it is up to you, since it is your project.

@gribozavr. Ask greenbank, he might be able to write a fast binary.

One more thing. I would recommend to all users that we work on +1 numbers than -1. We might find a factor of fermat number by doing so, which will be an added bonus to the twin prime.[/QUOTE]
I don't think we need to worry about the 13th power:

4^13 = 67,108,864
5^13 = 1,220,703,125
6^13 = 13,060,694,016 (13G)
7^13 = around 96G

The only odd k in the range 350M-25G is 5^13. It has already been eliminated by NewPGen (1220703125*2^195000+1 is divisible by 3).

That leaves the perfect squares, cubes, and 5th power.

Perfect squares are separated by at least 20,000 in the 100M range:
10,000^2 = 100,000,000
10,001^2 = 100,020,001
This means that the chance of a specific k being a perfect square is about 1 in 20,000. Eliminating them will give at most a 0.005% speed increase. Moreover, the greater the k value is, the lesser the chance of it being a perfect square.

(To verify this, take the derivative of x^2, which is 2x. If the square root of k is x, the chance of k being a perfect square is 1 in 2x).

Perfect cubes are even rarer, and they are separated by at least 750,000.

500^3 = 125,000,000
501^3 = 125,751,501

Eliminating them will give at most a 0.00014% speed increase. Like squares, the greater the k value is, the lesser the chance of it being a perfect cube.

edit:

In regards to searching for +1 instead of -1, I forgot to mention that the chance of finding a Femat divisor is almost nonexistant for large k's (above 1M). All of the top 20 fermat divisors are for small k's (less than 100)

[url]http://primes.utm.edu/top20/page.php?id=8[/url]

What's going on?
 

Hi

I'm working currently on the 720-750 M range, but now I see that eric_v has given up on the range "720-740 M" maybe he made a mistake, but now the website claims that "720-740 M" is "Availeable", so am I working on this range or not? Untill clearly verifyed what I'm working on or not, I'm going to work with the 321 project...

Regards

KEP

Ps. I suggest any "n" yielding a megaprime should be our next power to 2, this way we help find more huge primes, and we make a surtain winner for long among twins :)

I delete the row of table.