New milestone - Page 13

storm5510 · 2009-08-14, 01:25

Quote:

Originally Posted by ckdo

While I was out ...

Countdown to proving M(20996011) is the 40th Mersenne Prime: 400

20 days for 100 exponents this time...

I've been looking at this tread a while now. I must admit that I do not know what you're doing here. Isn't M40 going back a ways? M44 was in 2006.

TimSorbet · 2009-08-14, 01:31

Quote:

Originally Posted by storm5510

I've been looking at this tread a while now. I must admit that I do not know what you're doing here. Isn't M40 going back a ways? M44 was in 2006.

We know that M(20996011)=2^20996011-1 is prime, but we aren't 100% certain that it's the 40th Mersenne prime (M40). Once every Mersenne number smaller than M20996011 has been double checked, then we'll know for sure. This is what we're counting down. Once that hits 0, we'll know with an extremely high certainty (barring two tests randomly producing the same incorrect residue on a prime, the odds of which are astronomical) that M20996011 is the 40th Mersenne prime, M40.

cheesehead · 2009-08-14, 02:01

Let me add just a bit to Mini-Geek's explanation:

GIMPS assignments are not completed and reported in monotonic increasing order of exponent. Thus, there are always "gaps" among the GIMPS LL/DC results where an exponent's test has not yet completed even though larger exponents' tests are finished.

When this forum (or the milestones page) refers to "Countdown to proving M(20996011) is the 40th Mersenne Prime", that's the count of exponents less than 20996011 whose double-check assignments have not yet been successfully completed. The same goes for "Countdown to proving M(24036583) is the 41st Mersenne Prime", ...

Until that count reaches 0, there is some uncertainty as to whether there are any Mersenne primes with exponents between 13466917 (which we "know" to be M39 because we've done successful double-checks on all exponents below it) and 20996011.

Uncwilly · 2009-08-14, 02:14

Quote:

Originally Posted by storm5510

I've been looking at this tread a while now. I must admit that I do not know what you're doing here. Isn't M40 going back a ways? M44 was in 2006.

It is good that you asked that question. This is one that will be helpful for others looking at the thread.

storm5510 · 2009-08-14, 03:16

Okay, I get it. You're checking the gaps between tested exponents. That needs to be done without a doubt.

I started using P95 about five years ago, but didn't stay with it. I was running it on an 800 MHz P3. Trial factoring was taking weeks to do, so I returned everything and dropped out, but I knew I would be back when I had hardware that could handle the task.

10metreh · 2009-08-15, 10:42

BTW, how many exponents out of all the ones GIMPS has doublechecked would be expected to have an incorrect residue on both tests?

TimSorbet · 2009-08-15, 12:59

Quote:

Originally Posted by 10metreh

BTW, how many exponents out of all the ones GIMPS has doublechecked would be expected to have an incorrect residue on both tests?

Let's limit this to tests where no serious errors were reported
The chance of an incorrect residue on each is about 1.5%, (from The Math) so the chance of both being incorrect is .015*.015=0.000225=0.0225%, or one in 4,444.44... From http://www.mersenne.org/primenet/, GIMPS has DCd about 518010 candidates. 518010/4444=~116.56
Edit: this is for two incorrect residues, whether identical or not. I'm not fully sure which 10metreh was implying. The expected number of two incorrect tests having the same wrong residue should be about 116.56/2^64 =~ 6.31873*10^-18

ATH · 2009-08-15, 13:12

The chance that both checks have the same wrong residue when the doublecheck run is with a shift value is astronomically small, almost nonexistent.

http://www.mersenne.org/various/math.php

Quote:

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. Each squaring just doubles how much we have shifted the S value. Note that the mod 2P-1 step merely rotates the p-th bits and above to the least significant bits, so there is no loss of information. Why do we go to this trouble? If there were a bug in the FFT code, then the shifting of the S values ensures that the FFTs in the first primality test are dealing with completely different data than the FFTs in the second primality test. It would be near impossible for a programming bug to produce the same final 64 bit residues.

Uncwilly · 2009-08-17, 01:03

Quote:

Originally Posted by science_man_88

wonder if they can prove my challenge if so I whipped them see Challenge for more info

This is the wrong thread for your post.

ckdo · 2009-09-02, 23:02

Quote:

Originally Posted by ckdo

Countdown to proving M(20996011) is the 40th Mersenne Prime: 400

20 days for 100 exponents this time...

Countdown to proving M(20996011) is the 40th Mersenne Prime: 300

Again, 20 days for 100 exponents...

ckdo · 2009-10-07, 19:24

Quote:

Originally Posted by ckdo

Countdown to proving M(20996011) is the 40th Mersenne Prime: 300

Again, 20 days for 100 exponents...

Countdown to proving M(20996011) is the 40th Mersenne Prime: 200

34 days for 100 exponents...

2009-08-14, 02:01	#135
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 7692₁₀ Posts	Let me add just a bit to Mini-Geek's explanation: GIMPS assignments are not completed and reported in monotonic increasing order of exponent. Thus, there are always "gaps" among the GIMPS LL/DC results where an exponent's test has not yet completed even though larger exponents' tests are finished. When this forum (or the milestones page) refers to "Countdown to proving M(20996011) is the 40th Mersenne Prime", that's the count of exponents less than 20996011 whose double-check assignments have not yet been successfully completed. The same goes for "Countdown to proving M(24036583) is the 41st Mersenne Prime", ... Until that count reaches 0, there is some uncertainty as to whether there are any Mersenne primes with exponents between 13466917 (which we "know" to be M39 because we've done successful double-checks on all exponents below it) and 20996011. Last fiddled with by cheesehead on 2009-08-14 at 02:11 Reason: I gotta start putting this stuff in the wiki, even if not in very organized order.

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2009-08-14, 03:16	#137
storm5510 Random Account Aug 2009 Not U. + S.A. 3·953 Posts	Okay, I get it. You're checking the gaps between tested exponents. That needs to be done without a doubt. I started using P95 about five years ago, but didn't stay with it. I was running it on an 800 MHz P3. Trial factoring was taking weeks to do, so I returned everything and dropped out, but I knew I would be back when I had hardware that could handle the task.

2009-08-15, 10:42	#138
10metreh Nov 2008 912₁₆ Posts	BTW, how many exponents out of all the ones GIMPS has doublechecked would be expected to have an incorrect residue on both tests?