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 paulunderwood 2014-03-13 20:35

Primes found!

We have our first NeRDy prime as part of TOPS. The winning number, found by Chuck Lasher, is [URL="http://primes.utm.edu/primes/page.php?id=117418"]10^360360-10^183037-1[/URL], which has been verified prime by Chuck using PFGW. It will enter the [URL="http://primes.utm.edu/top20/page.php?id=15"]top20 Near-repdigits[/URL] as 12[SUP]th[/SUP] biggest.

:showoff:

 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 :toot:

Please attribute TOPS, Ksieve, LLR, PrimeForm (a.k.a OpenPFGW for the BLS part), of course, CHG in your new prover code.

According to [url]http://primes.utm.edu/bios/page.php?id=797[/url] 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

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).
[B]EDIT[/B]: just 3 iterations were sufficient. [URL="http://primes.utm.edu/primes/page.php?id=118734"]10^388080-10^112433-1 is prime[/URL].

Also, we have [URL="http://primes.utm.edu/primes/page.php?id=118732"]another 388k[/URL] prime, too. This one will be easily proved with PFGW.

 Batalov 2014-11-08 23:19

[QUOTE=paulunderwood;387163]According to [URL]http://primes.utm.edu/bios/page.php?id=797[/URL] the largest number proved with CHG was:

(4529^16381 - 1)/4528 ‏(‎59886 digits) via code CH2 on 12/01/2012[/QUOTE]
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 [URL="http://mada.la.coocan.jp/nrr/repunit/tm.cgi?p=733"]10^73260-1[/URL]) [URL="http://factordb.com/index.php?query=10^75516-10^2256-1"]75k digit prime[/URL] 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: [U]35477[/U]157ms. (that's ~10 hours for one iteration)
Running CHG with h = 16, u = 7. Right endpoint has 14861 digits.
Done! Time elapsed: [U]151834[/U]429ms. (that's ~[B]42 hours[/B]! for one iteration)
Running CHG with h = 15, u = 6. Right endpoint has 14651 digits.
Done! Time elapsed: [U]11931[/U]826ms.
...etc (43 steps)
[/CODE]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:

[URL="http://primes.utm.edu/primes/page.php?id=118983"]10^388080 - 10^332944 - 1 [/URL]

:banana:

 Batalov 2014-12-23 00:41

And forth:
[URL="http://primes.utm.edu/primes/page.php?id=118985"]10^388080 - 10^342029 - 1[/URL]
:george::george:

 paulunderwood 2014-12-23 00:44

[QUOTE=Batalov;390774]And forth:
[URL="http://primes.utm.edu/primes/page.php?id=118985"]10^388080 - 10^342029 - 1[/URL]
:george::george:[/QUOTE]

:shock: Congrats!

 Batalov 2015-01-17 04:16

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)

 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