Share N+/-1 Primality Proofs

[MisterBitcoin]

Added this PRP (302 digits), proved with N-1.

Notice: N-1 and N+1 are FF. Lucky hit.

[DukeBG]

this one is almost there, but you'll have to run a pretty big ecm/pm1 to add a factor to bring it over the top (primo cert would be likely faster)

[paulunderwood]

Originally Posted by DukeBG

this one is almost there, but you'll have to run a pretty big ecm/pm1 to add a factor to bring it over the top (primo cert would be likely faster)

I don't understand becuase factorDB reports:

Primality testing 146^537-145 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 8+sqrt(7)
Calling N-1 BLS with factored part 32.07% and helper 2.12% (98.39% proof) 146^537-145 is Fermat and Lucas PRP! (0.0505s+0.0000s)

Isn't 32.7+2.12> 33.33 or is there some overlap?

[DukeBG]

Yeah, i clicked that too. Not sure, but i think 33.33% is not a solid criteria and the success may vary.

[MisterBitcoin]

Originally Posted by DukeBG

this one is almost there, but you'll have to run a pretty big ecm/pm1 to add a factor to bring it over the top (primo cert would be likely faster)

N-1: prp32 = 38345427112016738375831313545761 (curve 334 stg2 B1=1000000 sigma=1829841937 thread=0)
Now its done.

[DukeBG]

beautiful!

[axn]

Originally Posted by paulunderwood

I don't understand becuase factorDB reports:



Isn't 32.7+2.12> 33.33 or is there some overlap?

Big part * 3 + small part >= 100 is the criteria. Not (big + small) * 3 > 100.

So 32.07*3 + 2.12 = 98.33 < 100 doesn't quite make it.

[chris2be8]

Here's a pair of PRPs in factordb where proving the smaller would enable a N-1 proof the larger is prime.

1100000001278844269 (2^3741-3757^16-1)/1298176050
1100000001273748953 2^3741-3757^16

Chris

[chris2be8]

Proving http://factordb.com/index.php?id=1100000001289043848 (389 digits) would enable a N-1 proof that (23^441*22+1)/177 http://factordb.com/index.php?id=1100000001288676864 (600 digits) is prime.

Chris

[MDaniello]

A bit of factoring allowed a N-1 proof of this 323 digit number, which in turn was a factor big enough to prove this 4368 digit number prime, again by N-1.

[DukeBG]

Originally Posted by MDaniello

A bit of factoring allowed a N-1 proof of this 323 digit number, which in turn was a factor big enough to prove this 4368 digit number prime, again by N-1.

Nice!