Great! Congrats!

M100,000,007
 

I have reached iteration 66,666,666. I have highlighted this iteration as well as the 66.666666% (2/3 of the way complete!!!) mark. I am still cranking away at 0.259 seconds per iteration and my expected completion date is December 14th!

Yxine: Have you reached 60 million yet? If so, please check your residue with my above post to make sure they compare.

The Countdown has begun for M100,000,007!!!
 

I have now reached iteration 70 million! I am expected to finish on December 15th, so 94 more days to go! The end is near...

[Tue Sep 12 04:48:48 2006]
Iteration 70,000,000 / 100,000,007
UID: StarQwest/StarQwest1, M100,000,007 interim Wc1 residue C757899056581F60 at iteration 70,000,000
UID: StarQwest/StarQwest1, M100,000,007 interim Wc1 residue 20C01EDA30E4408F at iteration 70,000,001
UID: StarQwest/StarQwest1, M100,000,007 interim Wc1 residue F32D852CB6B59CAA at iteration 70,000,002

Yxine: How close are you to reaching 70 million iterations? Please compare your double check residue for 60 million and then when you reach 70 million. Thanks.

The Log for M100,000,007:

As anyone following this test can see, it has been a huge effort on the part of myself and Yxine to test and double check this number. As far as I know, this is the largest mersenne number ever tested for primality. Here is the log for this test (with only the most important milestones listed). I will release the full results file (with every million iterations listed) after the test is complete.


[Tue Jan 10 9:55:09 2006]
Begin trial factoring to 2^72 of M100,000,007.

[Tue Jan 10 10:08:57 2006]
Factoring M100,000,007 to 2^63 is 100.000000% complete.

[Tue Jan 10 10:34:50 2006]
Factoring M100,000,007 to 2^64 is 100.000000% complete.

[Tue Jan 10 11:33:37 2006]
Factoring M100,000,007 to 2^65 is 100.000000% complete.

[Tue Jan 10 13:32:04 2006]
Factoring M100,000,007 to 2^66 is 100.000000% complete.

[Tue Jan 10 17:31:51 2006]
Factoring M100,000,007 to 2^67 is 100.000000% complete.

[Wed Jan 11 01:33:11 2006]
Factoring M100,000,007 to 2^68 is 100.000000% complete.

[Wed Jan 11 18:05:11 2006]
Factoring M100,000,007 to 2^69 is 100.000000% complete.

[Fri Jan 13 04:11:48 2006]
Factoring M100,000,007 to 2^70 is 100.000000% complete.

[Sun Jan 15 16:22:26 2006]
Factoring M100,000,007 to 2^71 is 100.000000% complete.

[Fri Jan 20 18:55:50 2006]
Factoring M100,000,007 to 2^72 is 100.000000% complete.

[Fri Jan 20 18:55:53 2006]
UID: StarQwest/StarQwest1, M100,000,007 no factor to 2^72, Wc1: BFC9997D

[Mon Jan 23 04:30:29 2006]
UID: StarQwest/StarQwest1, M100,000,007 stage 1 is 100.000000% complete.

[Sat Jan 28 11:40:16 2006]
UID: StarQwest/StarQwest1, M100,000,007 stage 2 is 100.000000% complete.

[Sat Jan 28 11:49:45 2006]
No factor found.
UID: StarQwest/StarQwest1, M100,000,007 completed P-1, B1=435,000, B2=12,288,750, Wc1: 1BDE3DBF

[Tue Jan 31 19:58:51 2006]
Iteration 1,000,000 / 100,000,007

[Thu Mar 02 18:25:18 2006]
Iteration 10,000,000 / 100,000,007

[Mon Apr 03 04:50:02 2006]
Iteration 20,000,000 / 100,000,007

[Thu May 04 19:01:44 2006]
Iteration 30,000,000 / 100,000,007

[Mon Jun 05 10:49:38 2006]
Iteration 40,000,000 / 100,000,007

[Fri Jul 07 06:06:20 2006]
Iteration 50,000,000 / 100,000,007

[Wed Aug 09 23:29:13 2006]
Iteration 60,000,000 / 100,000,007

[Tue Sep 12 04:48:48 2006]
Iteration 70,000,000 / 100,000,007

As you can see, trial factoring took 18 days and was unsuccessful, meaning that there is a possibility (800,000 : 1 odds) that M100,000,007 is prime!! Then, the LL test began, taking approximately one month per 10 million iterations.


The total time spent so far is as follows:

Trial factoring: 010 days, 09 hours, 00 minutes, 44 seconds
P-1 factoring: 007 days, 16 hours, 53 minutes, 52 seconds
LL testing: 226 days, 16 hours, 59 minutes, 03 seconds
Total: 244 days, 18 hours, 53 minutes, 39 seconds

These are the statistics up until the moment I reached iteration 70 million. At this rate, I have averaged 0.279822043 seconds per iteration, which is approximately 92.201% of the ideal speed (0.258 seconds per iteration). Wow, enough math for one day. Over and out.


P.S. If anyone is interested in joining my team (team StarQwest) and searching for M45, please reply to this messege.

By the way StarQwest, what kind of computer are you using to do this test? What FFT size is required?

[QUOTE=www.mersenne.org/math.htm]GIMPS double-checking goes a bit further to guard against programming errors. Prior to starting the Lucas-Lehmer test, the S0 value is left-shifted by a random amount.[/QUOTE]

Is that being done?

[QUOTE=jinydu;87379]By the way StarQwest, what kind of computer are you using to do this test? What FFT size is required?



Is that being done?[/QUOTE]

I am using a Pentium D 2.8 GHz computer (it has two cores, so I am running two versions of Prime95 simutaneously- one testing M100,000,007 and the other testing ~10 million digit numbers). As for the FFT size, I am not 100% sure, but I believe it to be 6144K. As for the doublecheck, I am not 100% sure exactly what has been done, but Yxine is doublechecking the exponent and we are comparing residues every 10 million iterations. So far, they have matched up until iteration 50 million. However, he would be able to tell you if the S0 value was shifted or not.

P.S. For anyone who cares, I am not at iteration 71,751,610. This is taking SOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO long! I just hope, after all this, that it is prime.

[quote=StarQwest;87416]I just hope, after all this, that it is prime.[/quote]StarQwest,

Just in case it's not prime, I want you to know that Yxine and you have my everlasting admiration for tackling it!

[QUOTE=cheesehead;87614]StarQwest,

Just in case it's not prime, I want you to know that Yxine and you have my everlasting admiration for tackling it![/QUOTE]

Thanks. I first came up with the idea back in early January. I had recently bought a Pentium D 2.8 Ghz computer, and I thought it would be fun to put Prime95 on it (I first joined GIMPS in September 2005). With the faster processer and more computing power, I thought it would be kind of cool to attempt to test a mersenne number larger than anyone else ever had. I first thought of doing a 100 million digit number, but when I benchmarked it and found that it would take nine years, I quickly changed my mind. I then looked up in the GIMPS database and found that the largest LL test ever completed was on M79,299,959 (the last prime exponent before 79.3 million). Knowing I would have to exceed what GIMPS was currently tracking, I looked in the 80 million range. Then I figured, the test wouldn't be truly memorable unless it was in a whole new ballpark, say, 100 million. Since a 100 million digit number was out of the question, I decided to try an exponent over 100 million. This was benchmarked to take eleven months- MUCH more managable. As it turned out, 100,000,007 is the first prime number over 100 million. It had been previously trial factored to 2^60, with no factor found. I decided to take this exponent (assigning it to myself by manually entering "Test=100000007,0,1" into the worktodo.ini file.) I then e-mailed George Woltman, letting him know I would be testing a number above the 79.3 million range, and he confirmed that this had never been done before. I then joined this forum (look at some of my earliest posts- they are of me trying to find out any information about M100,000,007). There were some people (in this forum) that didn't believe it was possible, but I set out to prove them wrong. So, on January 10th, 2006, at 9:55 AM EST, I began trial factoring M100,000,007 to 2^72. Ten days later, no factor was found so I began P-1 factoring it. Eight days after that, no factor was found, so I began the LL test. I hit iteration 1,000,000 on January 31st and iteration 50 million on July 7th. I am currently on iteration 72,654,000, and will finish sometime around December 14th. I will begin an "official" countdown when I hit iteration 99 million (three days before finishing). I will make a post when the test has 24 hours to go, 12 hours to go, 2 hours, 30 minutes, and five minutes. As soon as it finishes, I will immediately post the result, and will shortly thereafter post a jpeg image (similar to the other images in this thread) of Prime95 showing (and proving) the completion along with the complete results file and test log. The last I heard from Yxine, he said he would finish his doublecheck two weeks after mine finishes. I believe this test will count for approximately 65 P-90 CPU years, so I will really shoot up in the ranking!!!

P.S. If the number does return prime (wish me luck), I will not be allowed to post immediately after the test finishes due to the GIMPS and EFF rules and regulations regarding a new mersenne prime (especially one over 10 million digits). Yxine would confirm two weeks later, and an "official" confirmation shortly afterward. However, if for some reason I don't post exactly five minutes after I give the five minute countdown, don't go starting any rumors, because I will most likely post very soon (The chances are unfortunately 800,000 to 1 of the number being prime). However, if a couple days go by... Whatever happens, I'll try to keep everyone posted.

This morning I got to 60.000.000 iterations with the resudue 3B20D85B5B205CA7 that is equal to StarQwest one!!!

There were some periods when my computer had to be shutted down because of repair-works in the flat, so my "two weeks after" seams to become "three weeks after". Anyway, I continue to do a test with about 0.24 secs/iteration 24 hours a day :)

Also I made a simple "random-factorizer" on my web sites. The idea is that every hit a user checkes one random factor over M100.000.007. When he visits any page on the site, the script is generating "proper" divider for that number and makes a check. It is very fast, so users don't see any lost in loading time. If the factor is found, it is sending to my e-mail :) As there are about 5000 unique visitors per day (plus, a visitor visits few pages), this checking was already done about 1 million times. No factor yet :)

Interesting thing:
When testing script over exponents with known factors in M0-M1000 range, the factor is reporting about every 3.5 hours approximately

[QUOTE=Yxine;87644]The idea is that every hit a user checkes one random factor over M100.000.007. When he visits any page on the site, the script is generating "proper" divider for that number and makes a check. It is very fast, so users don't see any lost in loading time. If the factor is found, it is sending to my e-mail :) As there are about 5000 unique visitors per day (plus, a visitor visits few pages), this checking was already done about 1 million times. No factor yet :)[/QUOTE]

What is your website Yxine? And I wonder, can this can be modified to factor other Mersenne numbers (such as MM127 :wink: )?

[QUOTE=StarQwest;87620]I believe this test will count for approximately 65 P-90 CPU years, so I will really shoot up in the ranking!!!
[/QUOTE]

Where did you get the figure of 65 CPU years (I'm curious)? And I thought that Prime95 only allows testing of exponents up to 79.3 million.

This gives me an idea for another way to measure how much a user has contributed to GIMPS: How large must an exponent be in order for an LL test on that exponent to take as many CPU years as the user has contributed?

[QUOTE=jinydu;87651]
Where did you get the figure of 65 CPU years (I'm curious)? And I thought that Prime95 only allows testing of exponents up to 79.3 million.

This gives me an idea for another way to measure how much a user has contributed to GIMPS: How large must an exponent be in order for an LL test on that exponent to take as many CPU years as the user has contributed?[/QUOTE]

I know that testing a ten million digit number counts for ~7 CPU years. Since M100,000,007 is a 30.1 million digit number, it takes approximately 9 - 10 times longer to test than a ten million digit number. This would make the total work for this number ~63 - 70 CPU years. Also, just for numbers sake, testing M1,000,000,007 (which is also a prime exponent and has 300 million digits) would credit you about 7,000 CPU years (although such a test would take 100 years on my machine:surprised). Old versions of Prime95 only allow up to 79.3 million, but the newer versions (v24.14 and v24.13) allow you to test exponents up to 596 million (see my post on M595,999,993 (post 150 in this thread)). You have to manually enter them in the worktodo.ini file, but they will run, providing you have enough computer power to perform iterations on exponents of this size.

So you don't know of an exact formula for the number of CPU years that GIMPS will award for LL tests on exponents larger than 79.3 million?