Thread for posting tiny primes

[3.14159]

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

[CRGreathouse]

Originally Posted by 3.14159

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

What makes you say that?

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

[axn]

Originally Posted by 3.14159

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?

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

[3.14159]

Originally Posted by CRGreathouse

What makes you say that?

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

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

[CRGreathouse]

Originally Posted by 3.14159

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

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

[axn]

Originally Posted by 3.14159

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

How?!

[CRGreathouse]

Originally Posted by axn

How?!

I wondered the same thing -- that would seem to take 8 * 10¹⁰⁹⁹ divisions (actually modular exponentiations). But even if they were done by oracle we still wouldn't know much about the primality of the number.

[science_man_88]

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.

[rajula]

Originally Posted by axn

How?!

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 )

[CRGreathouse]

Originally Posted by 3.14159

M-R's weakness = Proth numbers.

You can prove any non-Proth 72-bit number prime with M-R.

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.

[science_man_88]

Originally Posted by CRGreathouse

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.

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