Thread: Primes found! View Single Post
2014-11-08, 23:19   #6
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

226178 Posts

Quote:
 Originally Posted by paulunderwood According to http://primes.utm.edu/bios/page.php?id=797 the largest number proved with CHG was: (4529^16381 - 1)/4528 ‏(‎59886 digits) via code CH2 on 12/01/2012
The records in CHG are not in the size but the % factored part, and I've played with that some years earlier.

Among other things, I have proven a relatively uninteresting, artificially constructed (around 25.2% factorization of 10^73260-1) 75k digit prime with CHG back in '11. It took literally weeks. I don't think I reported it, because I got bored and delayed the Prime proof of the dependent p8641. I finished it some time later when I could run a 32-thread linux Primo (in FactorDB, it is also proven by Ray C.).
Code:
n=10^75516-10^2256-1;
F=1;
G= 27457137299220528239776088787.....00000000000000;

Input file is:  TestSuite/P75k2.in
Certificate file is:  TestSuite/P75k2.out
Found values of n, F and G.
Number to be tested has 75516 digits.
Modulus has 20151 digits.
Modulus is 26.683667905153090234% of n.

NOTICE: This program assumes that n has passed
a BLS PRP-test with n, F, and G as given.  If
not, then any results will be invalid!

Square test passed for G >> F.  Using modified right endpoint.

Search for factors congruent to 1.
Running CHG with h = 16, u = 7. Right endpoint has 15065 digits.
Done!  Time elapsed:  35477157ms. (that's ~10 hours for one iteration)
Running CHG with h = 16, u = 7. Right endpoint has 14861 digits.
Done!  Time elapsed:  151834429ms. (that's ~42 hours! for one iteration)
Running CHG with h = 15, u = 6. Right endpoint has 14651 digits.
Done!  Time elapsed:  11931826ms.
...etc (43 steps)
Two things happened over three years: the computers got better, and Pari was made better! (and GMP that Pari uses can and probably uses AVX these days).

I was pleasantly surprised how fast the 388k prime (but of course 29.08%-factored) turned out to be. And just three iterations, too.