Share N+/-1 Primality Proofs - Page 12

Mathew · 2013-04-14, 11:43

Quote:

Originally Posted by Batalov

~~Three~~ Four free gifts for anyone (PRPs are by D.Broadhurst; just prove the N+1 10^3333+y cofactors with threaded Primo; they ECMd easily):
10^9999+658628^3-1
10^9999+1301728^3-1
10^9999+2877590^3-1
10^9999+1570022^3-1

These are now complete, however 10^9999+1301728^3-1 is stuck.

lorgix · 2013-04-14, 11:53

Quote:

Originally Posted by Mathew

These are now complete, however 10^9999+1301728^3-1 is stuck.

I added some small factors. It is now proven with P+1.

Puzzle-Peter · 2013-04-23, 19:13

There are dozens of PRPs with 58711 digits that could be proved using N+1. Unfortunately, it says "too big to prove atm"

Stargate38 · 2013-04-30, 00:31

That needs to be fixed (hopefully in the next 6 months). Anyway, I found this Proth prime with NewPGen and LLR:

731969*2⁹⁶⁹+1 (N-1)

I've attached my LLR results (n=2-1000, n=1000-2000) to this post. "FOSH" (base-36 for 731969=7*17*6151) is also the name of a species of birdlike alien from Star Wars.

Stargate38 · 2013-05-01, 19:05

Actually, I meant n=1000-10000, not 2000

kar_bon · 2013-05-01, 21:47

Quote:

Originally Posted by Stargate38

I've attached my LLR results (n=2-1000, n=1000-2000) to this post.

You missed the primes for n=3, 7 and 9. Use srsieve or pfgw instead to test/confirm for n<100 while newpgen won't find such small primes.

Stargate38 · 2013-05-01, 22:37

5855753, 93692033, and 374768129? Those are small numbers. I only consider the ones >M31. I used Proth to find more primes. Their base-36 values start with species names from Star Wars (I love the Saga and especially the Guide to Alien Species, which I have in my collection):

731969*36¹⁵-1
731969*36¹⁷-1
731969*36⁹⁹-1
731969*36¹⁵-1
731969*36¹⁷-1
731969*36⁹⁹-1
26350885*36⁵+1
26350885*36⁶+1
26350885*36⁸+1
26350885*36²⁷+1
26350885*36⁴⁸+1
26350885*36⁶⁵+1
26350885*36²⁶⁴+1
26350885*36⁵⁵¹+1
26350885*36²⁰⁰⁹+1
26350885*36²²²⁴+1
26350885*36⁴⁷⁷⁶+1
26350885*36⁵⁰⁶⁷+1

I'll post these and more primes in their own thread after I find more. Before I do that, however, I want to know if there is already a thread for this type of prime or not.

kar_bon · 2013-05-02, 08:25

Quote:

Originally Posted by Stargate38

I only consider the ones >M31.
[...]
26350885*36⁵+1
26350885*36⁶+1
[...]
I'll post these and more primes in their own thread after I find more. Before I do that, however, I want to know if there is already a thread for this type of prime or not.

26350885*36²+1 > M31 is prime, too.

There's no thread for such numbers.
CRUS is only searching for bases <= 1030 and special k-values.
I suggest to make your own page/list and search/find all primes for n>0, otherwise it's not valuable at all.

Stargate38 · 2013-05-02, 18:26

First, it's impossible to get all the primes for n>0 because there are an infinity of them. Second, I only want to go to n=10000 for now because my computer is much slower then yours. I'll have to get a ton of money built up for buying a new one, which could take years with the current economy (thus the limit of n=10000).

Do you know of any 100% free sites I could put my list on, such that it won't be deleted after 1-2 months of inactivity? I have a lot of side projects (3D modeling, simulations of planet formation, etc.).

kar_bon · 2013-05-02, 22:52

The expression "all primes for n>0" was meant to be of the form k*b^n+/-1 for your examples given with base 36 and k=731969 or k=26350885.
So like Mersenne primes 2^n-1 are always given for all n>0 not only greater than some limit.

For example of base-36 k-value:
26350885: 2, 5, 6, 8, 27, 48, 65, 264, 551, 2009, 2224, 4776, 5067 [10k]

No, I don't know any free site but there're some for a very small budget of 20 € / year.

Stargate38 · 2013-05-03, 13:34

There HAS to be a free site out there SOMEWHERE! I'm NOT paying to keep my numbers online!

2013-05-01, 19:05	#126
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 3·13·17 Posts	Typo in my post. Actually, I meant n=1000-10000, not 2000 Last fiddled with by Stargate38 on 2013-05-01 at 19:07

2013-05-01, 22:37	#128
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 3·13·17 Posts	Lots of primes! 5855753, 93692033, and 374768129? Those are small numbers. I only consider the ones >M31. I used Proth to find more primes. Their base-36 values start with species names from Star Wars (I love the Saga and especially the Guide to Alien Species, which I have in my collection): 73196936¹⁵-1 73196936¹⁷-1 73196936⁹⁹-1 73196936¹⁵-1 73196936¹⁷-1 73196936⁹⁹-1 2635088536⁵+1 2635088536⁶+1 2635088536⁸+1 2635088536²⁷+1 2635088536⁴⁸+1 2635088536⁶⁵+1 2635088536²⁶⁴+1 2635088536⁵⁵¹+1 2635088536²⁰⁰⁹+1 2635088536²²²⁴+1 2635088536⁴⁷⁷⁶+1 2635088536⁵⁰⁶⁷+1 I'll post these and more primes in their own thread after I find more. Before I do that, however, I want to know if there is already a thread for this type of prime or not. Last fiddled with by Stargate38 on 2013-05-01 at 22:38 Reason: replace "post" with "thread"

2013-05-02, 18:26	#130
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 1227₈ Posts	ALL primes n>0? You're kidding! There are an infinite number of them! First, it's impossible to get all the primes for n>0 because there are an infinity of them. Second, I only want to go to n=10000 for now because my computer is much slower then yours. I'll have to get a ton of money built up for buying a new one, which could take years with the current economy (thus the limit of n=10000). Do you know of any 100% free sites I could put my list on, such that it won't be deleted after 1-2 months of inactivity? I have a lot of side projects (3D modeling, simulations of planet formation, etc.). Last fiddled with by Stargate38 on 2013-05-02 at 18:30 Reason: Need free host for number list!

2013-05-03, 13:34	#132
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 297₁₆ Posts	I want a FREE SITE for my NUMBERS! There HAS to be a free site out there SOMEWHERE! I'm NOT paying to keep my numbers online!

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2013-04-23, 19:13	#124
Puzzle-Peter Jun 2009 2²×3²×19 Posts	There are dozens of PRPs with 58711 digits that could be proved using N+1. Unfortunately, it says "too big to prove atm"

2013-05-02, 22:52	#131
kar_bon Mar 2006 Germany 2904₁₀ Posts	The expression "all primes for n>0" was meant to be of the form k*b^n+/-1 for your examples given with base 36 and k=731969 or k=26350885. So like Mersenne primes 2^n-1 are always given for all n>0 not only greater than some limit. For example of base-36 k-value: 26350885: 2, 5, 6, 8, 27, 48, 65, 264, 551, 2009, 2224, 4776, 5067 [10k] No, I don't know any free site but there're some for a very small budget of 20 € / year.