[QUOTE=jinydu;87709]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?[/QUOTE]

No, I can only estimate based on the size of the exponent. A rough estimation would be:

((Digits in mersenne number / 10,000,000)^2) * 7 CPU years.

Thus, a 100 million digit number would be worth:

((100,000,000 / 10,000,000)^2) * 7 CPU years
=(10^2) * 7 CPU years
=700 CPU years
This is the one that would take nine years to test, so be warned. M100,000,007 only has 30.1 million digits, so it would count for ~63 CPU years using this formula.


Here is something interesting:

Speed of a P90 Computer: 32,980,719 floating point operations (calculations).

Thus, 1 CPU year = (32,980,719 calculations / sec)(86,400 sec / day)(365.25 days / year) = 1,040,792,337,914,400 calculations per year!:surprised Thus, a 10 million digit number (which counts for 7 CPU years) takes more than 7 quadrillion calculations to prove whether or not it is prime!!! (14 quadrillion if you count double checking!)

P.S. This also means that a one petaflop (1,000,000 gigaflop) supercomputer (one will most likely be built within the next couple of years) would be able to complete 1 CPU year every second, testing a ten million digit number every seven seconds! At this rate, a ten million digit prime would be expected to be found after 24 days, but a one hundred million digit number would take a staggering 66 years! A billion digit prime would take 66,000 years!!! Thus, we will need exaflops (10^9 gigaflops) and beyond to make operation billion digits succeed! Right now, GIMPS is at 22 teraflops (0.022 petaflops or 0.000022 exaflops).:glare: Still, in 10 or 20 years, who knows where we'll be...:cool:

[QUOTE=StarQwest;87740]Thus, 1 CPU year = (32,980,719 calculations / sec)(86,400 sec / day)(365.25 days / year) = 1,040,792,337,914,400 calculations per year!:surprised Thus, a 10 million digit number (which counts for 7 CPU years) takes more than 7 quadrillion calculations to prove whether or not it is prime!!! (14 quadrillion if you count double checking!)[/QUOTE]

If I'm not mistaken, one of the reasons that a P90 CPU year was chosen as the standard unit and remains in use today (long after the P90 computer is obselete) is because it is close to [tex]10^{15}[/tex] calculations. This allows for easy conversion from CPU years to basic calculations, and back.

[QUOTE=StarQwest;87740]P.S. This also means that a one petaflop (1,000,000 gigaflop) supercomputer (one will most likely be built within the next couple of years) would be able to complete 1 CPU year every second, testing a ten million digit number every seven seconds! At this rate, a ten million digit prime would be expected to be found after 24 days, but a one hundred million digit number would take a staggering 66 years! A billion digit prime would take 66,000 years!!! Thus, we will need exaflops (10^9 gigaflops) and beyond to make operation billion digits succeed! Right now, GIMPS is at 22 teraflops (0.022 petaflops or 0.000022 exaflops).:glare: Still, in 10 or 20 years, who knows where we'll be...:cool:[/QUOTE]

You seem to be making assumptions about what the density of Mersenne primes will be in those regions...

[QUOTE=jinydu;87757]You seem to be making assumptions about what the density of Mersenne primes will be in those regions...[/QUOTE]

I am using the overall odds of finding a mersenne prime. If you increase the size of the number by a factor of 10, it becomes approximately 1,000 times harder to find a prime because the LL tests take 100 times longer (10x more iterations and each iteration takes 10x longer) and the chances of finding a prime decrease by a factor of ten. For instance, a ten million digit number takes just over one month to test on my machine and the chances of it being prime are approximately 280,000 to one. On the other hand, a one hundred million digit number would take just over 100 months (8 - 9 years) to test and the chances of it being prime are approximately 2,800,000 to one. A billion digit number would take ~900 years to test the the chances of it being prime are approximately 28,000,000 to one.

M100,000,000
 

I have now reached iteration 75 million on M100,000,007! I am three-fourths of the way done!!! 4.3 million more iterations to go before I surpass the world record on the most iterations performed on a single exponent (current record is 79,299,959)! The entire test will finish on December 14.

[QUOTE=StarQwest;87819]If you increase the size of the number by a factor of 10, it becomes approximately 1,000 times harder to find a prime because the LL tests take 100 times longer (10x more iterations and each iteration takes 10x longer) and the chances of finding a prime decrease by a factor of ten.[/QUOTE]

Actually, if I am not mistaken, the amount of work needed to complete an exponent goes as [tex]n^2\log(n)[/tex], not [tex]n^2[/tex].

Also, are you sure that the chances of an exponent being prime decreases as [tex]\frac{1}{n}[/tex]?

[QUOTE=jinydu;88082]Actually, if I am not mistaken, the amount of work needed to complete an exponent goes as [tex]n^2\log(n)[/tex], not [tex]n^2[/tex].

Also, are you sure that the chances of an exponent being prime decreases as [tex]\frac{1}{n}[/tex]?[/QUOTE]

I am giving rough, order of magnitude estimates, for simplicity purposes. It is much easier for people to understand if you say it takes approximately 1,000 times more computer power to find a 100 million digit prime than a 10 million digit prime, as opposed to saying that it takes 932.9384769302012 times more power or saying that it takes 1,172.93820910 times more power. In actuality, it would take about 125 times longer to test a 100 million digit number than a 10 million digit one, but I just round it off to 100 for simplicity purposes. Furthermore, the chances decreasing as [tex]\frac{1}{n}[/tex] are also an approximation. Each time the number of digits increases by a factor of 10, the number of primes increases by approximately 6.2. Thus, you would expect 6.2(6) =37.2 primes less than one million digits and 6.2(7) = 43.4 primes less than 10 million digits, which is close to the actual values of 38 primes and 44 primes respectively. You could thus expect 49.6 primes less than 100 million digits. Therefore, the first 100 million digit prime will probably be the 50th mersenne prime, however this is only based on this probability. This probability follows the [tex]\frac{1}{n}[/tex] relationship, so I am basing my calculations on this.

[QUOTE=StarQwest;88074]I have now reached iteration 75 million on M100,000,007! I am three-fourths of the way done!!! 4.3 million more iterations to go before I surpass the world record on the most iterations performed on a single exponent (current record is 79,299,959)! The entire test will finish on December 14.[/QUOTE]

Great! I can make a login for you on my site so that you upload there your resudues to compare with my ones.

[QUOTE=Yxine;88167]Great! I can make a login for you on my site so that you upload there your resudues to compare with my ones.[/QUOTE]

What is the address for your site?

Noticed in an older thread that 100.0-100.1M has been factored to 50 bits. Has anyone factored this range >50bits? If not, I would like to Trial Fractor this range up to 62bits. Also, what is the status of the 100.1-100.2M range?

Regards,

Harlee

[QUOTE=StarQwest;88225]What is the address for your site?[/QUOTE]

[url]http://mp2006.larin.name[/url]

[b]2 Harlee[/b]

This range is done to 52 bits. You can take it to any desired range. Also it would be great if you submit your results to me for putting them in MasterPrime 2006 database

Yxine,

If these ranges have already been done to 52bits, where can I get a list of exponents that still needs to be trial factored within these ranges? I'm including the results I've done so far. These results were also sent to the [url]http://mersenne-aries.sili.net[/url] stats site.

Regards,

Harlee