Share N+/-1 Primality Proofs - Page 14

Puzzle-Peter · 2013-06-06, 05:36

Quote:

Originally Posted by firejuggler

(and sorry Puzzle-Peter, i snatched this one from you)

That's fine. They're only a few minutes of work each. But I must admit I was wondering about some of my certificates not being needed when I uploaded them.

Batalov · 2013-06-09, 00:36

38502*529^38502-1 ;-)

My first tiny GW prime. (Outside of FactorDB, it is proven of course.)

wblipp · 2013-09-08, 13:39

PRP list had 10^338*4+10^169*6+3

It's obviously 4x^2+6x+3, and P-1 factors as (2x+1)*(x+1)

I see other large PRPs from forms like this, but there are cofactors after removing small divisors, so the algebra doesn't work.

wblipp · 2013-10-16, 17:05

Spotted (311^898+1)/96722 in the PRP list today. The denominator is 311^2, so P-1 is (311^896-1). Helping factordb find the algebraic factors enabled the proof.

wblipp · 2013-10-18, 04:11

Found (2^9053+7)/39 in the PRP list. Adding the algebraic factors of (2^9048-1) enabled the N-1 proof.

Also (2^9066*67-1)/267, which needed algebraic factors from 2^9064-1 to enable the N-1 proof.

And (10^2731*7-67)/3

And (828^937-1)/827

And (2^9099+7)/15

10^2739+10^297-1 already had all the N+1 factors. All I did was press the proof button.

(2^9109*7+1)/15

lorgix · 2013-11-02, 21:21

I factored (5189^303+1)/(5189^101+1).
That enabled the N-1 proof of (5189^607-1)/5188.

YuL · 2013-11-06, 18:14

2^13645-511_<4108> was waiting for someone to click on the "Proof" button (N-1), I did it.

Batalov · 2013-11-06, 18:40

(10^6439*8-791)/9 also waited for a click (by N-1).

(I've found it in M.Kamada's primesize.txt list; and after that checked that Phi₆₄₃₇(10) has had a certificate since 2008. Factordb also had it on record.)

lorgix · 2013-11-06, 20:23

I factored 252^473-1.
That enabled the N-1 proof of (252^947-1)/251.

I'm doing a lot of these.

wblipp · 2013-11-10, 05:11

(2^27721*57-1)/113 and (2^27721*55-1)/109 needed the known factors (2^27720-1) added to the N-1. Fortunately doing the first automatically spilled over into the second.

YuL · 2013-11-10, 16:37

Factoring the remaining C109 in 2097^63-1 enabled the N-1 proof of (2097^757-1)/2096
The proofs of the following ones were enabled by adding algebraic factors to N-1 or N+1
2^8451-9 => N+1
(2^8461*91-1)/181 => N-1
(2^8465+3)/35 => N-1

2013-09-08, 13:39	#146
wblipp "William" May 2003 New Haven 93E₁₆ Posts	PRP list had 10^3384+10^1696+3 It's obviously 4x^2+6x+3, and P-1 factors as (2x+1)(x+1) I see other large PRPs from forms like this, but there are cofactors after removing small divisors, so the algebra doesn't work. Last fiddled with by wblipp on 2013-10-16 at 17:02 Reason: grammerr*

2013-10-16, 17:05	#147
wblipp "William" May 2003 New Haven 100100111110₂ Posts	Spotted (311^898+1)/96722 in the PRP list today. The denominator is 311^2, so P-1 is (311^896-1). Helping factordb find the algebraic factors enabled the proof. Last fiddled with by wblipp on 2013-10-16 at 17:06 Reason: algebra

2013-10-18, 04:11	#148
wblipp "William" May 2003 New Haven 93E₁₆ Posts	Found (2^9053+7)/39 in the PRP list. Adding the algebraic factors of (2^9048-1) enabled the N-1 proof. Also (2^906667-1)/267, which needed algebraic factors from 2^9064-1 to enable the N-1 proof. And (10^27317-67)/3 And (828^937-1)/827 And (2^9099+7)/15 10^2739+10^297-1 already had all the N+1 factors. All I did was press the proof button. (2^91097+1)/15 Last fiddled with by wblipp on 2013-10-18 at 05:47 Reason: Add additonal factorizations*

2013-11-10, 05:11	#153
wblipp "William" May 2003 New Haven 2×7×13² Posts	(2^2772157-1)/113 and (2^2772155-1)/109 needed the known factors (2^27720-1) added to the N-1. Fortunately doing the first automatically spilled over into the second. Last fiddled with by wblipp on 2013-11-10 at 05:13

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2013-06-09, 00:36	#145
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·7·677 Posts	38502*529^38502-1 ;-) My first tiny GW prime. (Outside of FactorDB, it is proven of course.)

2013-11-02, 21:21	#149
lorgix Sep 2010 Scandinavia 3×5×41 Posts	I factored (5189^303+1)/(5189^101+1). That enabled the N-1 proof of (5189^607-1)/5188.

2013-11-06, 18:14	#150
YuL Feb 2012 Paris, France 7·23 Posts	2^13645-511_<4108> was waiting for someone to click on the "Proof" button (N-1), I did it.

2013-11-06, 18:40	#151
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10010100000110₂ Posts	(10^6439*8-791)/9 also waited for a click (by N-1). (I've found it in M.Kamada's primesize.txt list; and after that checked that Phi₆₄₃₇(10) has had a certificate since 2008. Factordb also had it on record.)

2013-11-06, 20:23	#152
lorgix Sep 2010 Scandinavia 1147₈ Posts	I factored 252^473-1. That enabled the N-1 proof of (252^947-1)/251. I'm doing a lot of these.

2013-11-10, 16:37	#154
YuL Feb 2012 Paris, France 7·23 Posts	Factoring the remaining C109 in 2097^63-1 enabled the N-1 proof of (2097^757-1)/2096 The proofs of the following ones were enabled by adding algebraic factors to N-1 or N+1 2^8451-9 => N+1 (2^8461*91-1)/181 => N-1 (2^8465+3)/35 => N-1