M35 is 100th largest known prime
 

I see that the 35th Mersenne prime, the very first discovery of GIMPS, is about to be pushed off the list of the 100 largest known primes:
[url]http://primes.utm.edu/primes/search.php?Number=100[/url]

This was the first discovery made on a PC, while the previous few Mersennes had all been discovered on supercomputers. Just for fun, if you were searching for Mersenne primes from scratch, how long would it take for a single fast quad processor system of today to search from the beginning up to M1398269? I'm guessing around 1 year, assuming that you could eliminate around half of the candidates by factoring, but I would be interested if anyone has a better estimate.

I don't know, I'll have to try and figure that out later. I remember verifying all found up though the 70's or 80's (and I mean all, not factored) in a couple hours at the most on a single core of a 2.5 GHz Athlon (or was I still using my 1.6 GHz Athlon? I can't remember).

[quote=Mini-Geek;132087]I don't know, I'll have to try and figure that out later. I remember verifying all found up though the 70's or 80's (and I mean all, not factored) in a couple hours at the most on a single core of a 2.5 GHz Athlon (or was I still using my 1.6 GHz Athlon? I can't remember).[/quote]
Trial factoring pays big dividends. 5/8 is a good estimate of your chance
of finding one, using a tiny fraction of the time for an LLtest.
About 4 years ago I wrote my own programs for a K6 (using school
multiplication) and found all the Mersenne primes up to and including
Colquitt and Welsh's one (notable for showing up Slowinsky's gaps)

David

We need to take Bill Gates' advice and organize a project to factor some of these larger-prime-wannabes, in order to boost M35's ranking. "[url=http://en.wikipedia.org/wiki/All_your_base_are_belong_to_us]All your non-Mersenne primes are belong to us[/url]" [AYNMPABTU for short] or something like that.

Any volunteers?

[quote=ewmayer;132096]We need to take Bill Gates' advice and organize a project to factor some of these larger-prime-wannabes, in order to boost M35's ranking. "[URL="http://en.wikipedia.org/wiki/All_your_base_are_belong_to_us"]All your non-Mersenne primes are belong to us[/URL]" [AYNMPABTU for short] or something like that.

Any volunteers?[/quote]

Great idea, but there's a caveat: what if Bill's PFP (prime factorization project) produces SEVERAL primes larger than M35 for each of the 850000+ digit primes ?!

[QUOTE=m_f_h;132322]Great idea, but there's a caveat: what if Bill's PFP (prime factorization project) produces SEVERAL primes larger than M35 for each of the 850000+ digit primes ?![/QUOTE]
Easy - just keep crunching on those, um, "subprime factors", until you break them into smaller ones. [Requires Vista[sup]©[/sup] OS installation and MSFactorPrimes[sup]TM[/sup] Professional Premium Edition[sup]©[/sup] license upgrade].

Looks like it just fell to #101:
[url]http://primes.utm.edu/primes/search.php?Number=101[/url]
We'd better get to work on that factoring project.

[quote=ewmayer;132457]Easy - just keep crunching on those, um, "subprime factors", until you break them into smaller ones. [Requires Vista[sup]©[/sup] OS installation and MSFactorPrimes[sup]TM[/sup] Professional Premium Edition[sup]©[/sup] license upgrade].[/quote]
Nice... in fact, there's a whole new theory of "primeness" to develop:
a prime could be classified according to the number of times it can be broken into "subprime factors"... or in analogy to Erdös-Selfridge classification, the Gates classification: G(p) = 1+max{ G(s); s in subprime factors of the prime p }, and G(p)=0 if p has no subprime factors (it is conjectured that such p exist, so we add this clause "just in case", to ensure G(p) is always well-defined. ;-)
I fear there will never be a linux port of the relevant code...

[QUOTE=ewmayer;132096]We need to take Bill Gates' advice and organize a project to factor some of these larger-prime-wannabes, in order to boost M35's ranking. "[url=http://en.wikipedia.org/wiki/All_your_base_are_belong_to_us]All your non-Mersenne primes are belong to us[/url]" [AYNMPABTU for short] or something like that.

Any volunteers?[/QUOTE]

I'm confused...are you suggesting that some of the Top 100 primes may in fact be composite and that a concerted factoring effort is all that is required to prove it and get M35 back into the top 100?

[QUOTE=petrw1;132901]I'm confused...are you suggesting that some of the Top 100 primes may in fact be composite and that a concerted factoring effort is all that is required to prove it and get M35 back into the top 100?[/QUOTE]Hehe, look who got caught. Um, yeah, we need to factor those pesky top primes, so as to drop them drop the list. I'll start by suggesting they will all have at least [color=red][i]one[/i][/color] factor on common.