Mersenneforum calendar
 

[URL="http://www.mersenneforum.org/calendar.php"]calendar[/URL]... :smile:

*hmm* it shows "Tue, 19th January 2038" to me!

[QUOTE=TheJudger;228049]*hmm* it shows "Tue, 19th January 2038" to me![/QUOTE]

See [url]http://en.wikipedia.org/wiki/Year_2038_problem[/url]

And has been discussed previously on the forum.

Jacob

It's a pre-emptive celebration of my 55th birthday, no doubt. (No, it's the date that time_t rolls over, I think...)

And now to take the thread wildly off-topic! I wasn't kidding, that day really will be my 55th birthday. My birthday actually is 19830119... a prime number. M19830119 is composite, and we seem to have at least one factor for it. Is there a decent/reasonable way for me to finish factoring M19830119? I suppose there is no value in the complete factorization other than a personal curiosity, but it might be "neat" to have my birthday Mersenne fully factored. ;)

[QUOTE=KingKurly;228096]M19830119 is composite, and we seem to have at least one factor for it. Is there a decent/reasonable way for me to finish factoring M19830119?[/QUOTE]

No. Even if you do find another factor, the cofactor will almost certainly be composite. And if it were prime, we would have no way of proving it within the lifetime of the universe with current algorithms and hardware because it would not be a Mersenne (and thus it would not be LL-testable).

It's not very likely you can fully factor it and, as 10metreh points out, there is no chance of proving the primality of the ultimate factor. If you got very lucky you might fully factor the number with a probable-prime test on the ultimate factor. But if you work out just how lucky you would have to be, you will probably be dissuaded from trying. You have to be lucky enough that the second largest factor is within range of Trial Factoring, P-1, and ECM. Look up the 2-parameter Dickman Function to figure out how lucky that is.

[quote=wblipp;228147]It's not very likely you can fully factor it and, as 10metreh points out, there is no chance of proving the primality of the ultimate factor. If you got very lucky you might fully factor the number with a probable-prime test on the ultimate factor. But if you work out just how lucky you would have to be, you will probably be dissuaded from trying. You have to be lucky enough that the second largest factor is within range of Trial Factoring, P-1, and ECM. Look up the 2-parameter Dickman Function to figure out how lucky that is.[/quote]There is actually a very very small chance of proving primality. Let the cofactor be [I]q[/I]. [B]If[/B] [I]q[/I]+1 and/or [I]q[/I]-1 are exceptionally smooth apart from at most one large prime factor, and if that factor itself has the same property, right the way down to a point where there is no large prime factor [B]then[/B] it would be possible to prove primality.

The expected chance of this happening is in the range 0 < probability <= utterly insignificant.

Paul

Fun with birthdays and GIMPS assignments
 

[quote=KingKurly;228096]It's a pre-emptive celebration of my 55th birthday, no doubt. (No, it's the date that time_t rolls over, I think...)

And now to take the thread wildly off-topic! I wasn't kidding, that day really will be my 55th birthday. My birthday actually is 19830119... a prime number. M19830119 is composite, and we seem to have at least one factor for it. Is there a decent/reasonable way for me to finish factoring M19830119? I suppose there is no value in the complete factorization other than a personal curiosity, but it might be "neat" to have my birthday Mersenne fully factored. ;)[/quote]

See [URL]http://www.mersenneforum.org/showpost.php?p=228009&postcount=619[/URL] for some inspiration on how you could work your birthday into GIMPS. Test exponents of the form 830119xx or 83119xxx, or how about checking whether there are any exponents of the form 19830119x available (note that such an exponent will likely take a good while to test even on a newer PC). Since you're turning 28 (like me), you could grab some of the remaining 2828xxxx double checks. Etc. Etc. Unfortunately, the American style of writing your birthday - 01191983 - isn't really a good number for GIMPS, unless you're into ECM factoring, in which case you could do numbers of the form 119xxxx, or even 11983xx, or even 1191983 (if it happens to be prime).

Another idea, depending on your horsepower: take the entire 119M range one bit deeper in TF.