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 2014-03-13, 20:35 #1 paulunderwood     Sep 2002 Database er0rr 1101101011012 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     Apr 2010 Over the rainbow 2,473 Posts Congratz! 360360 digits? nice!
 2014-11-08, 07:20 #3 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 23×5×229 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 66558 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 100011110010002 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

23·5·229 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 32·389 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 23C816 Posts And forth: 10^388080 - 10^342029 - 1
2014-12-23, 00:44   #9
paulunderwood

Sep 2002
Database er0rr

32·389 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 23·5·229 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 916010 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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