Share N+/-1 Primality Proofs - Page 8

lorgix · 2012-03-02, 08:31

Quote:

Originally Posted by henryzz

What have people checked from the numbers I posted? I can check some more tomorrow.

I have proven many of the numbers you've posted.

Not many in the last file, yet.

firejuggler · 2012-03-02, 08:37

(11^1724*5+1)/6-1 need help with (11^431*3+3)/1516829834365402334277715308 or (11^862*3+3)/992082412380769750967560817656886431636998
(10^1627*14+13)/603+1 need (10^1625*25+11)/4141336702683390924663927819 factors
(10^1631*14-41)/99-1 need help with either(10^815+1)/(10^163+1) or(10^815-1)/(10^163-1)
(2^5358*175-1)/111-1) need help with (2^2677*5+1)/23300488449386234700116099
((2^5434*135+1)/79+1) need help with (2^1810*3+1)/1115755075968493924957
(2^5440*177+1)/591329-1 is FF but has a PRP1615 (proded, no luck)
((10^1731-1)*911/999+10^1731)/273-1 is FF but has a PRP1715(proded, no luck)
((10^1742*5+31)/1262187+1)/6534662+1 is FF, PRP1725 (proded, no luck)
((10^1841*79-7)/340407-1)/233854+1 is FF PRP1825 (proded, no luck)

and I poked a number of other (mainly 8-20 digits prime)

firejuggler · 2012-03-02, 10:21

Test finished!
PFGW output:

Primality testing (11^2577-1)/(11^859-1)/133 [N-1, Brillhart-Lehmer-Selfridge]
Prime_Testing_Warning, unused factor from helper file: 61 Prime_Testing_Warning, unused factor from helper file: 826129 Running N-1 test using base 7
Calling Brillhart-Lehmer-Selfridge with factored part 33.44% (11^2577-1)/(11^859-1)/133 is prime! (0.2408s+0.0001s)Proven by combined N+1/N-1-method

wblipp · 2012-03-03, 23:39

Henry,

I think the provable primes from your lists have been proven. But I see there are still easy pickings for higher numbers. I jacked the digit count up and scanned less than 200 PRPs before spotting (2^10069*19+1)/39. Are you going to extend your search to higher PRPs?

And just below it was (10^3031*35-359)/9

wblipp · 2012-03-04, 04:32

Quote:

Originally Posted by wblipp

I think the provable primes from your lists have been proven.

Double checking, I found some in the first list that could still be completed. I believe these really are as complete as possible with algebraic factors and the known factordb results. I haven't double checked the other lists yet.

wblipp · 2012-03-04, 19:41

Some 3 for 1 opportunities gleaned from Henry's Post #75. A Primo proof of the first number will enable a N+/-1 proof of the second number which will enable an N+/-1 proof of the third number.

(((2^6616*11-1)/35+1)/18978-1)/218489095992628142393749204529429310
((2^6616*11-1)/35+1)/18978
(2^6616*11-1)/35

(((10^1841*79-7)/340407-1)/233854+1)/12767374
((10^1841*79-7)/340407-1)/233854
(10^1841*79-7)/340407

(((10^1742*5+31)/1262187+1)/6534662+1)/423806
((10^1742*5+31)/1262187+1)/6534662
(10^1742*5+31)/1262187

This came from the same source, but I cannot find a third prime in the chain:
(((10^1731-1)*911/999+10^1731)/273-1)/107767440900618
((10^1731-1)*911/999+10^1731)/273

lorgix · 2012-03-04, 20:23

Edwin Hall uploaded a certificate for a prp1139 that emerged from (9636^1093-1)/9635-1. This allowed me to prove a p4351.

I've been adding several such numbers lately. The one closest to a proof is (5995^1009-1)/5994. N-1 is 32.79% factored.

I don't think these are proven before, since the [base]>[5*the exponent].

Batalov · 2012-03-05, 19:21

Quote:

Originally Posted by lorgix

The one closest to a proof is (5995^1009-1)/5994. N-1 is 32.79% factored.

Use Konyagin-Pomerance test with >30% factored, and the C-H-G method all the way down to 26.0% (and a bit below).

The fun part is doing Konyagin-Pomerance test from scratch. The PN-ACP book has its description, it's short and sweet. Or you can get existing recipes from the yahoo primeform discussion group - but this is less fun.

henryzz · 2012-03-05, 21:39

I might search higher digits. Downloading the numbers in pages of 1000 gets tedious quickly.
If someone provides me with the list of prps then I can put virtually any amount through my program.

firejuggler · 2012-03-05, 21:44

factordb can give you the entire list of prp, if you click the right link...

henryzz · 2012-03-05, 21:47

Quote:

Originally Posted by firejuggler

factordb can give you the entire list of prp, if you click the right link...

Whoops!! Didn't reallize it was in downloads. Will do it now.

2012-03-02, 08:37	#79
firejuggler Apr 2010 Over the rainbow 2³×5²×13 Posts	(11^17245+1)/6-1 need help with (11^4313+3)/1516829834365402334277715308 or (11^8623+3)/992082412380769750967560817656886431636998 (10^162714+13)/603+1 need (10^162525+11)/4141336702683390924663927819 factors (10^163114-41)/99-1 need help with either(10^815+1)/(10^163+1) or(10^815-1)/(10^163-1) (2^5358175-1)/111-1) need help with (2^26775+1)/23300488449386234700116099 ((2^5434135+1)/79+1) need help with (2^18103+1)/1115755075968493924957 (2^5440177+1)/591329-1 is FF but has a PRP1615 (proded, no luck) ((10^1731-1)911/999+10^1731)/273-1 is FF but has a PRP1715(proded, no luck) ((10^17425+31)/1262187+1)/6534662+1 is FF, PRP1725 (proded, no luck) ((10^184179-7)/340407-1)/233854+1 is FF PRP1825 (proded, no luck) and I poked a number of other (mainly 8-20 digits prime) Last fiddled with by firejuggler on 2012-03-02 at 09:07

2012-03-02, 10:21	#80
firejuggler Apr 2010 Over the rainbow 2600₁₀ Posts	Test finished! PFGW output: Primality testing (11^2577-1)/(11^859-1)/133 [N-1, Brillhart-Lehmer-Selfridge] Prime_Testing_Warning, unused factor from helper file: 61 Prime_Testing_Warning, unused factor from helper file: 826129 Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 33.44% (11^2577-1)/(11^859-1)/133 is prime! (0.2408s+0.0001s)Proven by combined N+1/N-1-method Last fiddled with by firejuggler on 2012-03-02 at 10:22

2012-03-03, 23:39	#81
wblipp "William" May 2003 New Haven 93E₁₆ Posts	Henry, I think the provable primes from your lists have been proven. But I see there are still easy pickings for higher numbers. I jacked the digit count up and scanned less than 200 PRPs before spotting (2^1006919+1)/39. Are you going to extend your search to higher PRPs? And just below it was (10^303135-359)/9 Last fiddled with by wblipp on 2012-03-03 at 23:52 Reason: Add second

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2012-03-04, 19:41	#83
wblipp "William" May 2003 New Haven 2·7·13² Posts	Some 3 for 1 opportunities gleaned from Henry's Post #75. A Primo proof of the first number will enable a N+/-1 proof of the second number which will enable an N+/-1 proof of the third number. (((2^661611-1)/35+1)/18978-1)/218489095992628142393749204529429310 ((2^661611-1)/35+1)/18978 (2^661611-1)/35 (((10^184179-7)/340407-1)/233854+1)/12767374 ((10^184179-7)/340407-1)/233854 (10^184179-7)/340407 (((10^17425+31)/1262187+1)/6534662+1)/423806 ((10^17425+31)/1262187+1)/6534662 (10^17425+31)/1262187 This came from the same source, but I cannot find a third prime in the chain: (((10^1731-1)911/999+10^1731)/273-1)/107767440900618 ((10^1731-1)*911/999+10^1731)/273

2012-03-04, 20:23	#84
lorgix Sep 2010 Scandinavia 3·5·41 Posts	Edwin Hall uploaded a certificate for a prp1139 that emerged from (9636^1093-1)/9635-1. This allowed me to prove a p4351. I've been adding several such numbers lately. The one closest to a proof is (5995^1009-1)/5994. N-1 is 32.79% factored. I don't think these are proven before, since the [base]>[5*the exponent].

2012-03-05, 21:39	#86
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 2³·3·5·7² Posts	I might search higher digits. Downloading the numbers in pages of 1000 gets tedious quickly. If someone provides me with the list of prps then I can put virtually any amount through my program.

2012-03-05, 21:44	#87
firejuggler Apr 2010 Over the rainbow 2³·5²·13 Posts	factordb can give you the entire list of prp, if you click the right link...