Well; 10^(2^162) + 1 = PRP?

[QUOTE=3.14159;231199]Well; 10^(2^162) + 1 = PRP?[/QUOTE]

What makes you say that?

Edit: A random number of that size without any prime factors below 10^500 has a 4 * 10[sup]-47[/sup] chance of being prime, so the trial division doesn't help here. The odds raise to 10[sup]-46[/sup] if it has no prime factors below 10^1000, so continuing the effort still won't give you much confidence.

[QUOTE=3.14159;231193]Looking at the tables.. I should look at a wider range of k's. No divisor for GF(162, 10) for k up to 300000, for 2^163

I'm going to try 300k to 1M for the k-range.

Tips, anyone?[/QUOTE]

Looking at the factors found in that page, looks like Geoff swept all of them till k=100G.

[QUOTE=CRGreathouse;231200]What makes you say that?

Edit: A random number of that size without any prime factors below 10^500 has a 4 * 10[sup]-47[/sup] chance of being prime, so the trial division doesn't help here. The odds raise to 10[sup]-46[/sup] if it has no prime factors below 10^1000, so continuing the effort still won't give you much confidence.[/QUOTE]

Well, now that I've finished checking all numbers below 1150 digits... No divisors there.

[QUOTE=3.14159;231241]Well, now that I've finished checking all numbers below 1150 digits... No divisors there.[/QUOTE]

OK, that takes primality 'probability' to 1.09 * 10[SUP]-47[/SUP]. If you can check for all factors below a million digits the odds rise to almost 10[SUP]-44[/SUP].

[QUOTE=3.14159;231241]Well, now that I've finished checking all numbers below 1150 digits... No divisors there.[/QUOTE]

How?!

[QUOTE=axn;231264]How?![/QUOTE]

I wondered the same thing -- that would seem to take 8 * 10[SUP]1099[/SUP] divisions (actually modular exponentiations). But even if they were done by oracle we still wouldn't know much about the primality of the number.

yeah the fact that the 2 post are 7 hours 20 minutes apart at best makes me skeptical he did any by hand let alone anything else.

[QUOTE=axn;231264]How?![/QUOTE]

I have the impression that 3.14 is testing numbers of the form k*2^m+1 with some small range of k's. That would fit the earlier posts and his use of the expression "no factors below x digits". (But of course you noticed this and just want to point out the silly claim :smile:)

[QUOTE=3.14159;231183]M-R's weakness = Proth numbers.

You can prove any non-Proth 72-bit number prime with M-R.[/QUOTE]

I'm still trying to understand the first statement. I clocked Pari at 24.8 microseconds per M-R test on a random 72-bit Proth prime, and 25.7 microseconds on a non-Proth prime. (They were 3388145912153815121921 and the following prime.) It seems like the times are statistically identical, and even if not the Proth in this case was faster.

[QUOTE=CRGreathouse;231289]I'm still trying to understand the first statement. I clocked Pari at 24.8 microseconds per M-R test on a random 72-bit Proth prime, and 25.7 microseconds on a non-Proth prime. (They were 3388145912153815121921 and the following prime.) It seems like the times are statistically identical, and even if not the Proth in this case was faster.[/QUOTE]

ms = micro seconds ? or do you know a trick you haven't said lol.