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 2014-03-13, 20:35 #1 paulunderwood     Sep 2002 Database er0rr 2·32·13·17 Posts Primes found! We have our first NeRDy prime as part of TOPS. The winning number, found by Chuck Lasher, is 10^360360-10^183037-1, which has been verified prime by Chuck using PFGW. It will enter the top20 Near-repdigits as 12th biggest.
 2014-03-13, 20:39 #2 firejuggler     "Vincent" Apr 2010 Over the rainbow 52678 Posts Congratz! 360360 digits? nice!
 2014-11-08, 07:20 #3 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×3,229 Posts Well, what do you know. I have one, and it's a toughie: only 29% factored N+1. Will have to give it a crack with CHG.gp script. (I've proven some primes with CHG before, but never this big. The percentage is pretty good though, the convergence will be fast.)
 2014-11-08, 07:27 #4 paulunderwood     Sep 2002 Database er0rr 2×32×13×17 Posts Congrats Please attribute TOPS, Ksieve, LLR, PrimeForm (a.k.a OpenPFGW for the BLS part), of course, CHG in your new prover code. 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 Last fiddled with by paulunderwood on 2014-11-08 at 08:53
 2014-11-08, 17:26 #5 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×3,229 Posts Two primes for the 388080 series Overnight, one iteration of CHG came through! Now, there's a good chance that we will have a proof (based on the %-age, we will need maybe 6-7 iterations; and I sacrificed factors of N-1 to make the proof actually shorter: the CHG proof needs only one pass if G or F == 1). EDIT: just 3 iterations were sufficient. 10^388080-10^112433-1 is prime. Also, we have another 388k prime, too. This one will be easily proved with PFGW. Last fiddled with by Batalov on 2014-11-08 at 20:36 Reason: both proofs finished
2014-11-08, 23:19   #6
Batalov

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

3·3,229 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.

 2014-12-22, 17:14 #7 paulunderwood     Sep 2002 Database er0rr 76128 Posts Congrats to Serge Batalov for finding the 3rd prime for the exponent 388080: 10^388080 - 10^332944 - 1
 2014-12-23, 00:41 #8 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3·3,229 Posts And forth: 10^388080 - 10^342029 - 1
2014-12-23, 00:44   #9
paulunderwood

Sep 2002
Database er0rr

1111100010102 Posts

Quote:
 Originally Posted by Batalov And forth: 10^388080 - 10^342029 - 1
Congrats!

Last fiddled with by paulunderwood on 2014-12-23 at 00:54 Reason: UTM said 388081, but now corrected to 388080

 2015-01-17, 04:16 #10 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3·3,229 Posts a NeRDs-related twin pair A small but elegant twin pair (using one "7" and two "7"s, with the rest of digits being "9"s): 10^4621-2*10^4208-1 is prime 10^4621-2*10^4208-3 is prime (Prime certificate is available)
 2015-01-18, 19:13 #11 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3·3,229 Posts And here is its evil twin: i.e. all digits are "7"s, except for one and two "9"s. (7*10^10014+18*10^3046+11)/9 (PRP) and (7*10^10014+18*10^3046-7)/9 (PRP) ECPP proofs are in progress. There is also a 6655-digit pair using only "3"s and "1"s (proven primes) (10^6655-6*10^4147-7)/3 (10^6655-6*10^4147-1)/3 M.Kamada collects these records.

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