Questions about twin prime search

jasong · 2006-06-06, 01:19

I've noticed in the twin prime search, the primes are of the form k*2^n+/-1, but has anyone thought of the possibility of +/-3, or any other odd number for that matter? I don't pretend to understand the limitations, or strengths, of the software, but what about searches involving, for instance, 2^195000+/-c where c is an odd number other than 1?

John Renze · 2006-06-06, 02:13

There are good reasons why +/-1 is required. Read up on these algorithms at:

http://primes.utm.edu/prove/index.html

The twin prime search is using the "classical methods" described in Section 3.

jasong · 2006-07-30, 02:42

Sorry to dredge up an old topic, but unless +/-3 takes significantly longer, and "significant," in my opinion, is AT LEAST 5-10 times as long as +/-1, I think it would be EXTREMELY worthwhile to explore "-3".

I volunteer for that task, shouldn't take me very long at all.

Edit: Ok, I can't figure out how to test -3, since the value I ASSUMED had to be changed didn't seem to accomplish anything. Going to pfgw.

MooMoo2 · 2006-07-30, 07:11

Quote:

Originally Posted by jasong

Sorry to dredge up an old topic, but unless +/-3 takes significantly longer, and "significant," in my opinion, is AT LEAST 5-10 times as long as +/-1, I think it would be EXTREMELY worthwhile to explore "-3".

I volunteer for that task, shouldn't take me very long at all.

Edit: Ok, I can't figure out how to test -3, since the value I ASSUMED had to be changed didn't seem to accomplish anything. Going to pfgw.

Twin primes are separated by 2, so a +/-3 prime would not be a twin prime (the primes would be separated by 6).

2006-07-30, 11:04

Jasong means testing +3 if +1 is prime and -3 if -1 is prime.
But it just don't take 5-10 times longer to test those. It is really impossible to test -3 them for true primality unless you factor 33% of -4 or -2. And that is not gonna happen.

You just can do a prp test, and maybe you show that the number is prp. That doesn't even take longer than -1/+1 but it is not possible to verify it prime.

R. Gerbicz · 2006-07-30, 11:26

Quote:

Originally Posted by thommy

Jasong means testing +3 if +1 is prime and -3 if -1 is prime.

Then this is really *GIBBERISH*, because by sieving we know that k*2^n+-1 isn't divisible by 3. So k*2^n+-3 will be divisible by 3 and >3 so those two numbers are composites!

jasong · 2006-07-30, 19:28

Quote:

Originally Posted by R. Gerbicz

Then this is really *GIBBERISH*, because by sieving we know that k*2^n+-1 isn't divisible by 3. So k*2^n+-3 will be divisible by 3 and >3 so those two numbers are composites!

It doesn't matter anyway, because this morning, too late to undo it, I realized that since the +/-3 didn't go through sieving, even if they weren't divisible by 3, no sieving decreased the chances of those few numbers being prime to almost nothing.

Btw, can we please stop calling misunderstandings gibberish? It isn't appreciated from Mr. Silverman, and it isn't appreciated now. As an analogy, what if you were a foreigner learning English, and used the term "learn" instead of "teach?" It would make perfect sense to someone who didn't understand the grammar rules well in English. I could, instead of acknowledging they lacked a key fact, call it gibberish, and maybe discourage them. Or I could simply correct them and move on.

I've never learned the ins and outs of looking at a formula and predicting the types of factors it could or could not have, and I really don't feel stupid for it. Calling my post gibberish was elitist and mean.

'nuff said.

Jens K Andersen · 2006-07-30, 21:49

Quote:

Originally Posted by MooooMoo

Twin primes are separated by 2, so a +/-3 prime would not be a twin prime (the primes would be separated by 6).

This is called sexy primes. The record is 10154 digits on a form which is easy to prove but takes longer to prp and sieve than k*2^n+/-1.

KlausLange · 2006-12-14, 11:46

Hi,

a very interesting project.

My question:

If you look at the project home page, you see the "News", but the last one dates from 27-11-06, its not really new...

A other thread says, that the project reached more than 200 normal primes.

I think for every 100 detected prime numbers it will be a good news and shows that the Home Page is still on time...

Grettings,
Klaus Lange

jmblazek · 2006-12-14, 14:47

Quote:

Originally Posted by KlausLange

Hi,

If you look at the project home page, you see the "News", but the last one dates from 27-11-06, its not really new...

I agree KlausLange...not a very "user friendly" home page. It could use some updating but I don't think they have the time. It's still quite manual. It's the best they have to offer right now.

They haven't even updated the Join page to include the automated PrimeGrid way of participating. Also, there's really no need to include the NewPGen step anymore as they already provide the pre-sieved files (which I think is preferable) sieved by Gribozavr.

Currently you'll have to search through the threads to get progress and up-to-date news. If you head over to PrimeGrid you can see their real-time progress in the ranges Rytis reserves.

Sieving is being done to 25G as the probability of finding a prime by then is 85%. Progress right now is 1.45G/25G or 5.8%. 208 primes have been reported to TPS. PG has already found an additional 28 primes that haven't been reported to TPS because their ranges are not yet completed...see the manual process.

This increase in visibility is just recently for the project…so a little time to adjust I think is needed. They’ve been pushed into the spotlight pretty quickly. They went from a dozen or so users to at least 5 times that in the past few weeks and it will be at least 5 times more that when PG TPS goes live.

BTW, welcome to the project!

pacionet · 2006-12-14, 15:02

Eh eh, you are right but I have also a work, a life, etc...

I update the site some times in my spare time ...

Sorry !

2006-06-06, 01:19	#1
jasong "Jason Goatcher" Mar 2005 6663₈ Posts	Questions about twin prime search I've noticed in the twin prime search, the primes are of the form k*2^n+/-1, but has anyone thought of the possibility of +/-3, or any other odd number for that matter? I don't pretend to understand the limitations, or strengths, of the software, but what about searches involving, for instance, 2^195000+/-c where c is an odd number other than 1?

2006-07-30, 02:42	#3
jasong "Jason Goatcher" Mar 2005 3·7·167 Posts	Sorry to dredge up an old topic, but unless +/-3 takes significantly longer, and "significant," in my opinion, is AT LEAST 5-10 times as long as +/-1, I think it would be EXTREMELY worthwhile to explore "-3". I volunteer for that task, shouldn't take me very long at all. Edit: Ok, I can't figure out how to test -3, since the value I ASSUMED had to be changed didn't seem to accomplish anything. Going to pfgw. Last fiddled with by jasong on 2006-07-30 at 02:46

2006-07-30, 11:04	#5
thommy 3738₁₀ Posts	Jasong means testing +3 if +1 is prime and -3 if -1 is prime. But it just don't take 5-10 times longer to test those. It is really impossible to test -3 them for true primality unless you factor 33% of -4 or -2. And that is not gonna happen. You just can do a prp test, and maybe you show that the number is prp. That doesn't even take longer than -1/+1 but it is not possible to verify it prime. Last fiddled with by thommy on 2006-07-30 at 11:05

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2006-06-06, 02:13	#2
John Renze Nov 2005 60₈ Posts	There are good reasons why +/-1 is required. Read up on these algorithms at: http://primes.utm.edu/prove/index.html The twin prime search is using the "classical methods" described in Section 3.

2006-12-14, 11:46	#9
KlausLange Dec 2006 2²·3 Posts	Hi, a very interesting project. My question: If you look at the project home page, you see the "News", but the last one dates from 27-11-06, its not really new... A other thread says, that the project reached more than 200 normal primes. I think for every 100 detected prime numbers it will be a good news and shows that the Home Page is still on time... Grettings, Klaus Lange

2006-12-14, 15:02	#11
pacionet Oct 2005 Italy 3×113 Posts	Eh eh, you are right but I have also a work, a life, etc... I update the site some times in my spare time ... Sorry !