Share N+/-1 Primality Proofs - Page 3

Batalov · 2011-11-24, 05:50

How 'bout this? 2837!^2+2837!+1 (a.k.a. Phi(3,2837!) )

This one will be a bit harder (will need some more factoring and a CHG on it) - Phi(5,2415!)

These extend A051856 and A200906

wblipp · 2011-11-24, 15:56

Quote:

Originally Posted by Batalov

How 'bout this? 2837!^2+2837!+1 (a.k.a. Phi(3,2837!)

How'd ya do dat? Factordb says it has an N-1 proof, but N-1 shows no known factors.

Batalov · 2011-11-24, 20:59

Well, in the same way as Phi(3,6001!) :-]

(just submitted it to a worker for a PRP test -- and the FactorDB apparently finds all 6001! factors one by one because it takes an inordinate amount of time, but when it does, it realizes that N-1 with the next prime is in order)

RichD · 2011-11-25, 16:23

Spotted (10^1296*13-7)/123 in the PRP list. Applying the algebraic factors to N-1 was not quite enough to prove it prime, but a few clicks on the scan button provided the one more needed factor.

RichD · 2011-11-26, 02:20

Another cute one (2^5367*7+1)/57 was proven by N-1 method.

<Taking a break for the night.>

Edit: (10^1621*77-41)/729 by N-1.

Batalov · 2011-11-26, 06:53

Quote:

Originally Posted by RichD

Another cute one (2^5367*7+1)/57 was proven by N-1 method.

<Taking a break for the night.>

Edit: (10^1621*77-41)/729 by N-1.

Well, in the same way as Phi(3,7606!) :-]

<Taking a break for the night.>

Batalov · 2011-11-26, 08:09

Phi(3,7076!) :-] in fact...

wblipp · 2011-11-26, 16:10

(10^1365*88-97)/9 by N+1 by adding the algebraic factors of 10^1365-1

RichD · 2011-11-28, 21:23

(5^2498+1)/26 is proven prime by applying the algebraic factors of 5^2496-1 to N-1.

(191*2^6105-1)/381 is proven prime by applying the algebraic factors of 2^6104-1 to N-1.

RichD · 2011-11-28, 23:40

(10^1900+3)/7 is proven prime by applying the algebraic factors of 10^1899+1 to N+1.

cmd · 2011-11-29, 00:13

Quote:

Originally Posted by Batalov

Phi(3,7076!) :-] in fact...

then ...

2011-11-26, 02:20	#27
RichD Sep 2008 Kansas 2⁴×211 Posts	Another cute one (2^53677+1)/57 was proven by N-1 method. <Taking a break for the night.> Edit: (10^162177-41)/729 by N-1. Last fiddled with by RichD on 2011-11-26 at 02:40 Reason: Add one more.

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2011-11-24, 05:50	#23
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×7×677 Posts	How 'bout this? 2837!^2+2837!+1 (a.k.a. Phi(3,2837!) ) This one will be a bit harder (will need some more factoring and a CHG on it) - Phi(5,2415!) These extend A051856 and A200906

2011-11-24, 20:59	#25
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·7·677 Posts	Well, in the same way as Phi(3,6001!) :-] (just submitted it to a worker for a PRP test -- and the FactorDB apparently finds all 6001! factors one by one because it takes an inordinate amount of time, but when it does, it realizes that N-1 with the next prime is in order)

2011-11-25, 16:23	#26
RichD Sep 2008 Kansas 3376₁₀ Posts	Spotted (10^1296*13-7)/123 in the PRP list. Applying the algebraic factors to N-1 was not quite enough to prove it prime, but a few clicks on the scan button provided the one more needed factor.

2011-11-26, 08:09	#29
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9478₁₀ Posts	Phi(3,7076!) :-] in fact...

2011-11-26, 16:10	#30
wblipp "William" May 2003 New Haven 2×7×13² Posts	(10^1365*88-97)/9 by N+1 by adding the algebraic factors of 10^1365-1

2011-11-28, 21:23	#31
RichD Sep 2008 Kansas 110100110000₂ Posts	(5^2498+1)/26 is proven prime by applying the algebraic factors of 5^2496-1 to N-1. (191*2^6105-1)/381 is proven prime by applying the algebraic factors of 2^6104-1 to N-1.

2011-11-28, 23:40	#32
RichD Sep 2008 Kansas 6460₈ Posts	(10^1900+3)/7 is proven prime by applying the algebraic factors of 10^1899+1 to N+1.