Base-6 speed for prime testing vs. base-2 - Page 2

jasong · 2010-07-22, 21:10

JoeO took a lot of credit for it. But Tumo(fine, that's his name) did a HUGE chunk of the work.

Edit: I may have misquoted him on his mathematical theories(some are hypotheses, but still useful when trying to find primes, since it's mostly just the testing that's scientific, not the choosing of values to test)

Edit2:Please don't try to contact him beyond Mersenne Forum, he doesn't do his research for notoriety and very much values his privacy.

Edit3: Didn't realize how long it's been since he's been on Mersenne Forum, so I left a pounce for him on IRC. His logons on IRC are rather unpredictable, so it might be anywhere from a few minutes to a few days before he sees my pounce. Oh, and he isn't Tumo on irc, so if you discover someone named Tumo on there it's a coincidence.(unless he has a handle I don't know about)

Tumo · 2010-07-25, 07:12

Hi everyone.
I hear and read from the above you've had questions about what's going on.

First, please allow me to make a few corrections to the posts from Jasong, his intentions are good but sometimes the lack of a strong math background gets in the way.

Joe O *and* I did it... Please do understand, Joe O (with whom I do remain in contact regularly) did the erat sieve and a few of the other base 2 bit fiddling tricks. He is SUPERB at that. When it comes to math, he IS better than I am. No doubting that.

JJsieve is the final name for was WAS 'PRS'... and those of you around and involved should remember PRS061, etc and all those test releases. Only when Joe did the final work while I had to step away did he rename a version to jjsieve, which was just fine with me. any name that works is fine! You remember it, right? Then it good with me.

As for the info on the primes which were found. Jasong did get that partly incorrect. The part he got incorrect and the reason you did not hear about it is because of who owns the rights to the FPGA / (super-GPU) built in 2005 as an Opteron 250 co-processor emulator in a 940 pin pack... it complies with the HT and all the protocols for a slave processor in a 2xx series cpu. The Mobo was the key part... main memory had to be accessed via CPU 0 (the Opt 250) and the slave (FPGA coprocessor) could only access it's private memory. CPU 0 also had private memory (like the old VME days, but much more limited.... the slave was a true slave. Since I was an employee of the company at the time, and my hobby of prime searching for RS was at a 'medium' participation level, I used what I knew ( pfgw, LLR, and all the sievers that existed at that time). The number did exceed 10 Megadigits, but it belonged to the company, not me and hence ineligible for submittal to EFF. I did develop a siever for Riesel's use, but B2 didn't like it. it was a Matrix based (square wheel) sieve instead of a bucket sieve (which Geoff has pulled off so very nicely!). I had the output format of factors backwards Easily fixed but he still found faults... oh well, I tried, but it worked and was considerably faster than what we had at the time (Proth Sieve by Mikael). AND, for what it's worth... the math was simple... base 6 because it was base 2 and base 3 (look up your basic Wheel sieve in the wikipedia if you don't know what this is). and the properties you can apply instantly to the candidate list! The rest is quite straight forward with the Bernstein prime number generator used to generate P's up to 10^15 (or so) at the time.

I should have come here sooner. Didn't realize there was so much you wanted to know. A lot of you see and use some of the things I've either developed or been lead engineer on every day, but that's not why I do it. Most of the things I did in the late 90's and early 2000's are now going into 2nd / 3rd generation product development. Why, you ask? I do it to help people. period.

So. I'm no quack but do have my limits and obey them. I have my PhD in EE/CE with some backup in Mathematics. I still have to break out the books for reference on some calc because I don't use it every day... I prefer to know WHERE the answers are and not always remember each answer. When that doesn't work, I call a REAL mathematician!! I'm NOT stupid!

I'll subscribe to this thread and feel free to ask questions. I would like this cleared up once and for all. We all have more important things to do than beat up on people.

For those who simply enjoy bashing.... try bashing out a 'primorial primorial' if you can call it that.... It's a twist on a Sylvester Sequence which generates a HUGE number of primes sequences using (and Euclid numbers / Euclid-Mullin) recurrence. Yes, you can write a nice custom sieve for what you want EASILY. that's the beauty of it. Go. Read, Enjoy, Learn, and APPLY.... Heck, why not go find a 20M or a 30M digit prime and prove it yourself given the pure definition of these sequences?... Heck, claim the 100M digit prize George is king, no doubt, his hand written/tuned (instruction timing counted) FFTS ARE THE BEST for their range limit, but I'm sure George, like any of us, enjoys a friendly peer challenge... AND WOULD PROBABLY LOVE SOMEONE WHO *CAN* CONTRIBUTE!

Ask George if he's willing to go 64-bit native based bignums and you help him do it IN ASSEMBLER or C (no C++ crap here)? Let's get this prime s*** out of the stone ages! we've been riding on the coat tails of the greats for far too long. Time to help out. I'm game and trying to do my part.

Cheers,
C.

10metreh · 2010-07-25, 07:33

Quote:

Originally Posted by Tumo

The number did exceed 10 Megadigits

So what was it?

Tumo · 2010-07-25, 07:37

Sorry to put you in the middle my friend. I should have remembered to come here and a) bounce the ideas of the gang and b) help you out. Sorry work has kept me so busy.

C.

kar_bon · 2010-07-25, 08:04

Quote:

Originally Posted by Tumo

Why, you ask? I do it to help people. period.

Quote:

Originally Posted by Tumo

Yes, you can write a nice custom sieve for what you want EASILY. that's the beauty of it. Go. Read, Enjoy, Learn, and APPLY.... Heck, why not go find a 20M or a 30M digit prime and prove it yourself given the pure definition of these sequences?

You want to help people first and suggest, to write a primefinder themselves next!?

So if it's so easy to find a 20M or 30M digit primes, why do you this first and show the result (and earn the price)?

It's correct, Euclid /Euclid-Mullin are climbing fast in digits per index.
But: the proof of primeness not (by now) easy at all.

So you are able to check those numbers prime easily?

Short: There were many like you, posting they found a big prime or can easily generate some records, but none of them were able to give an example of such Mega-prime, nor their new methods they use like proving prime!

Sorry, but nothing you told about, will be accepted until you give more details/programs/tests/results here!

jasong · 2010-07-25, 15:33

Kar bon, it takes years to test a 100M-digit prime. Even if he found 100 of him it'll still be another 2-3 years before a checksum can be provided.

Besides, prime-finding is mostly luck anyways, some of his hypotheses generate huge amounts of primes and anything that can improve the statistical chance of finding a large prime is awesome, even if it isn't strictly proven.

Edit: There's still the matter of that twin prime exponent I advised everyone to use on here. Maybe now someone would be willing to start a project?

10metreh · 2010-07-25, 17:26

I repeat: What was the 10M digit prime?

Tumo · 2010-07-25, 18:41

I'm sorry but i couldn't give you the exact number even if i remembered it exactly because it belonged to the company (was found and proven on company equipment & time)... they own the rights to it. I did ask for permission to publish it, but it denied. Their reasoning was disclosing the number and the required cpu time would show what the equipment could do but more so the characteristics of a few numbers we found in that range. It would show how quickly such numbers could be found and hint too heavily at what we were using them for.

What I remember and am probably ok to tell you is the K was 13xxxxxxxx and was (I'm pretty certain) prime. The N was somewhere around 48.5m and 48.8m and was a +1 (Proth). It had been one of those K's where the initial NPG sieve dropped the candidate list down to a few 10,000 and somewhere in the 16-20T range, the rest just peeled off leaving only a couple of candidates. The real target was the characteristics of the resulting pseudoprime when they were the a & b primes in it. We did the verification on the SGI 3000 in the lab.

I'm up to helping find it independently again or something else in that huge range. I know there were numbers we rejected all the way up to the limit of a standard 32 bit signed int because they didn't meet our criteria.

What should we do?

C

kar_bon · 2010-07-25, 19:48

Quote:

Originally Posted by Tumo

I'm sorry but i couldn't give you the exact number even if i remembered it exactly because it belonged to the company (was found and proven on company equipment & time)... they own the rights to it.

So the company only gets rights on hardware and time? What about the code?

If that code can easily find such huge prime, why not find some by yourself with about 3M digits? The prove can be done in 1 or 2 days for one number!

And me again: give an evidence of such a program.
Otherwise it's only rumour!

Quote:

Originally Posted by Tumo

It would show how quickly such numbers could be found and hint too heavily at what we were using them for.

This means 'your' company has found several of them, perhaps more and more every day?
I mean: If such numbers will generated by almost nothing (your comment implies this), this could be a great publicity to them, glory for the company -> money!
Only given a few numbers of them (it's easy to generate bigger ones) would no problem in my eyes! Only to show they can do without giving the code!

The other side would be: the phrase "what we were using them for" stands for some illegal!?
Rumors, too but suitable!

CRGreathouse · 2010-07-25, 19:57

Anyone want to buy a bridge? I can make you a great deal...

kar_bon · 2010-07-25, 20:05

Quote:

Originally Posted by CRGreathouse

Anyone want to buy a bridge? I can make you a great deal...

Some years ago, the german news brought this:

"New York will buy the Eiffel Tower!"

(Hint: it was April, 1st!)

2010-07-22, 21:10	#12
jasong "Jason Goatcher" Mar 2005 3·7·167 Posts	JoeO took a lot of credit for it. But Tumo(fine, that's his name) did a HUGE chunk of the work. Edit: I may have misquoted him on his mathematical theories(some are hypotheses, but still useful when trying to find primes, since it's mostly just the testing that's scientific, not the choosing of values to test) Edit2:Please don't try to contact him beyond Mersenne Forum, he doesn't do his research for notoriety and very much values his privacy. Edit3: Didn't realize how long it's been since he's been on Mersenne Forum, so I left a pounce for him on IRC. His logons on IRC are rather unpredictable, so it might be anywhere from a few minutes to a few days before he sees my pounce. Oh, and he isn't Tumo on irc, so if you discover someone named Tumo on there it's a coincidence.(unless he has a handle I don't know about) Last fiddled with by jasong on 2010-07-22 at 21:55

2010-07-25, 07:12	#13
Tumo Jan 2005 19 Posts	Greeting at last. Hi everyone. I hear and read from the above you've had questions about what's going on. First, please allow me to make a few corrections to the posts from Jasong, his intentions are good but sometimes the lack of a strong math background gets in the way. Joe O and I did it... Please do understand, Joe O (with whom I do remain in contact regularly) did the erat sieve and a few of the other base 2 bit fiddling tricks. He is SUPERB at that. When it comes to math, he IS better than I am. No doubting that. JJsieve is the final name for was WAS 'PRS'... and those of you around and involved should remember PRS061, etc and all those test releases. Only when Joe did the final work while I had to step away did he rename a version to jjsieve, which was just fine with me. any name that works is fine! You remember it, right? Then it good with me. As for the info on the primes which were found. Jasong did get that partly incorrect. The part he got incorrect and the reason you did not hear about it is because of who owns the rights to the FPGA / (super-GPU) built in 2005 as an Opteron 250 co-processor emulator in a 940 pin pack... it complies with the HT and all the protocols for a slave processor in a 2xx series cpu. The Mobo was the key part... main memory had to be accessed via CPU 0 (the Opt 250) and the slave (FPGA coprocessor) could only access it's private memory. CPU 0 also had private memory (like the old VME days, but much more limited.... the slave was a true slave. Since I was an employee of the company at the time, and my hobby of prime searching for RS was at a 'medium' participation level, I used what I knew ( pfgw, LLR, and all the sievers that existed at that time). The number did exceed 10 Megadigits, but it belonged to the company, not me and hence ineligible for submittal to EFF. I did develop a siever for Riesel's use, but B2 didn't like it. it was a Matrix based (square wheel) sieve instead of a bucket sieve (which Geoff has pulled off so very nicely!). I had the output format of factors backwards Easily fixed but he still found faults... oh well, I tried, but it worked and was considerably faster than what we had at the time (Proth Sieve by Mikael). AND, for what it's worth... the math was simple... base 6 because it was base 2 and base 3 (look up your basic Wheel sieve in the wikipedia if you don't know what this is). and the properties you can apply instantly to the candidate list! The rest is quite straight forward with the Bernstein prime number generator used to generate P's up to 10^15 (or so) at the time. I should have come here sooner. Didn't realize there was so much you wanted to know. A lot of you see and use some of the things I've either developed or been lead engineer on every day, but that's not why I do it. Most of the things I did in the late 90's and early 2000's are now going into 2nd / 3rd generation product development. Why, you ask? I do it to help people. period. So. I'm no quack but do have my limits and obey them. I have my PhD in EE/CE with some backup in Mathematics. I still have to break out the books for reference on some calc because I don't use it every day... I prefer to know WHERE the answers are and not always remember each answer. When that doesn't work, I call a REAL mathematician!! I'm NOT stupid! I'll subscribe to this thread and feel free to ask questions. I would like this cleared up once and for all. We all have more important things to do than beat up on people. For those who simply enjoy bashing.... try bashing out a 'primorial primorial' if you can call it that.... It's a twist on a Sylvester Sequence which generates a HUGE number of primes sequences using (and Euclid numbers / Euclid-Mullin) recurrence. Yes, you can write a nice custom sieve for what you want EASILY. that's the beauty of it. Go. Read, Enjoy, Learn, and APPLY.... Heck, why not go find a 20M or a 30M digit prime and prove it yourself given the pure definition of these sequences?... Heck, claim the 100M digit prize George is king, no doubt, his hand written/tuned (instruction timing counted) FFTS ARE THE BEST for their range limit, but I'm sure George, like any of us, enjoys a friendly peer challenge... AND WOULD PROBABLY LOVE SOMEONE WHO CAN CONTRIBUTE! Ask George if he's willing to go 64-bit native based bignums and you help him do it IN ASSEMBLER or C (no C++ crap here)? Let's get this prime s*** out of the stone ages! we've been riding on the coat tails of the greats for far too long. Time to help out. I'm game and trying to do my part. Cheers, C. Last fiddled with by Tumo on 2010-07-25 at 07:34 Reason: a few typos.

2010-07-25, 07:37	#15
Tumo Jan 2005 19 Posts	Dear Jasong Sorry to put you in the middle my friend. I should have remembered to come here and a) bounce the ideas of the gang and b) help you out. Sorry work has kept me so busy. C.

2010-07-25, 15:33	#17
jasong "Jason Goatcher" Mar 2005 3×7×167 Posts	Kar bon, it takes years to test a 100M-digit prime. Even if he found 100 of him it'll still be another 2-3 years before a checksum can be provided. Besides, prime-finding is mostly luck anyways, some of his hypotheses generate huge amounts of primes and anything that can improve the statistical chance of finding a large prime is awesome, even if it isn't strictly proven. Edit: There's still the matter of that twin prime exponent I advised everyone to use on here. Maybe now someone would be willing to start a project? Last fiddled with by jasong on 2010-07-25 at 15:34

2010-07-25, 18:41	#19
Tumo Jan 2005 10011₂ Posts	I'm sorry but i couldn't give you the exact number even if i remembered it exactly because it belonged to the company (was found and proven on company equipment & time)... they own the rights to it. I did ask for permission to publish it, but it denied. Their reasoning was disclosing the number and the required cpu time would show what the equipment could do but more so the characteristics of a few numbers we found in that range. It would show how quickly such numbers could be found and hint too heavily at what we were using them for. What I remember and am probably ok to tell you is the K was 13xxxxxxxx and was (I'm pretty certain) prime. The N was somewhere around 48.5m and 48.8m and was a +1 (Proth). It had been one of those K's where the initial NPG sieve dropped the candidate list down to a few 10,000 and somewhere in the 16-20T range, the rest just peeled off leaving only a couple of candidates. The real target was the characteristics of the resulting pseudoprime when they were the a & b primes in it. We did the verification on the SGI 3000 in the lab. I'm up to helping find it independently again or something else in that huge range. I know there were numbers we rejected all the way up to the limit of a standard 32 bit signed int because they didn't meet our criteria. What should we do? C Last fiddled with by Tumo on 2010-07-25 at 18:42

2010-07-25, 17:26	#18
10metreh Nov 2008 2×3³×43 Posts	I repeat: What was the 10M digit prime?

2010-07-25, 19:57	#21
CRGreathouse Aug 2006 3·1,993 Posts	Anyone want to buy a bridge? I can make you a great deal...

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Bases 2 & 4 reservations/statuses/primes	Jean Penné	Conjectures 'R Us	466	2021-07-25 04:05
Base 13 prime found	Siemelink	Conjectures 'R Us	0	2009-10-05 18:27
Riesel base 3 new testing idea	gd_barnes	Conjectures 'R Us	10	2008-12-20 00:19
mini-drive for high-n testing on Sierp base 4	gd_barnes	Conjectures 'R Us	43	2008-07-16 10:12
Speed of P-1 testing vs. Trial Factoring testing	eepiccolo	Math	6	2006-03-28 20:53