20140313, 20:35  #1 
Sep 2002
Database er0rr
2·7·281 Posts 
Primes found!
We have our first NeRDy prime as part of TOPS. The winning number, found by Chuck Lasher, is 10^36036010^1830371, which has been verified prime by Chuck using PFGW. It will enter the top20 Nearrepdigits as 12^{th} biggest.

20140313, 20:39  #2 
"Vincent"
Apr 2010
Over the rainbow
2,683 Posts 
Congratz! 360360 digits? nice!

20141108, 07:20  #3 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
59×163 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.) 
20141108, 07:27  #4 
Sep 2002
Database er0rr
2·7·281 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 20141108 at 08:53 
20141108, 17:26  #5 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
59·163 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 67 iterations; and I sacrificed factors of N1 to make the proof actually shorter: the CHG proof needs only one pass if G or F == 1).
EDIT: just 3 iterations were sufficient. 10^38808010^1124331 is prime. Also, we have another 388k prime, too. This one will be easily proved with PFGW. Last fiddled with by Batalov on 20141108 at 20:36 Reason: both proofs finished 
20141108, 23:19  #6  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
59·163 Posts 
Quote:
Among other things, I have proven a relatively uninteresting, artificially constructed (around 25.2% factorization of 10^732601) 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 32thread linux Primo (in FactorDB, it is also proven by Ray C.). Code:
n=10^7551610^22561; 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 PRPtest 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) I was pleasantly surprised how fast the 388k prime (but of course 29.08%factored) turned out to be. And just three iterations, too. 

20141222, 17:14  #7 
Sep 2002
Database er0rr
2×7×281 Posts 
Congrats to Serge Batalov for finding the 3rd prime for the exponent 388080:
10^388080  10^332944  1 
20141223, 00:41  #8 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010110010001_{2} Posts 

20141223, 00:44  #9  
Sep 2002
Database er0rr
2×7×281 Posts 
Quote:
Last fiddled with by paulunderwood on 20141223 at 00:54 Reason: UTM said 388081, but now corrected to 388080 

20150117, 04:16  #10 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
59·163 Posts 
a NeRDsrelated twin pair
A small but elegant twin pair (using one "7" and two "7"s, with the rest of digits being "9"s):
10^46212*10^42081 is prime 10^46212*10^42083 is prime (Prime certificate is available) 
20150118, 19:13  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
59×163 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*10^30467)/9 (PRP) ECPP proofs are in progress. There is also a 6655digit pair using only "3"s and "1"s (proven primes) (10^66556*10^41477)/3 (10^66556*10^41471)/3 M.Kamada collects these records. 
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