Primes found!

paulunderwood · 2014-03-13, 20:35

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 12^th biggest.

firejuggler · 2014-03-13, 20:39

Congratz! 360360 digits? nice!

Batalov · 2014-11-08, 07:20

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.)

paulunderwood · 2014-11-08, 07:27

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

Batalov · 2014-11-08, 17:26

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.

Batalov · 2014-11-08, 23:19

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.

paulunderwood · 2014-12-22, 17:14

Congrats to Serge Batalov for finding the 3rd prime for the exponent 388080:

10^388080 - 10^332944 - 1

Batalov · 2014-12-23, 00:41

And forth:
10^388080 - 10^342029 - 1

paulunderwood · 2014-12-23, 00:44

Quote:

Originally Posted by Batalov

And forth:
10^388080 - 10^342029 - 1

Congrats!

Batalov · 2015-01-17, 04:16

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)

Batalov · 2015-01-18, 19:13

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.

2014-03-13, 20:35	#1
paulunderwood Sep 2002 Database er0rr 2×7⁴ 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 12^th biggest.

2014-11-08, 07:27	#4
paulunderwood Sep 2002 Database er0rr 1001011000010₂ 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 San Diego, Calif. 2×3×1,733 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

2015-01-17, 04:16	#10
Batalov "Serge" Mar 2008 San Diego, Calif. 289E₁₆ 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): 10^4621-210^4208-1 is prime 10^4621-210^4208-3 is prime (Prime certificate is available)

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2014-03-13, 20:39	#2
firejuggler "Vincent" Apr 2010 Over the rainbow B6B₁₆ Posts	Congratz! 360360 digits? nice!

2014-11-08, 07:20	#3
Batalov "Serge" Mar 2008 San Diego, Calif. 24236₈ 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.)

2014-12-22, 17:14	#7
paulunderwood Sep 2002 Database er0rr 2·7⁴ 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 San Diego, Calif. 2·3·1,733 Posts	And forth: 10^388080 - 10^342029 - 1

2015-01-18, 19:13	#11
Batalov "Serge" Mar 2008 San Diego, Calif. 2·3·1,733 Posts	And here is its evil twin: i.e. all digits are "7"s, except for one and two "9"s. (710^10014+1810^3046+11)/9 (PRP) and (710^10014+1810^3046-7)/9 (PRP) ECPP proofs are in progress. There is also a 6655-digit pair using only "3"s and "1"s (proven primes) (10^6655-610^4147-7)/3 (10^6655-610^4147-1)/3 M.Kamada collects these records.