Share N+/-1 Primality Proofs

[chris2be8]

Thanks to whoever did the last one, I've just found another case:

Proving http://factorization.ath.cx/index.ph...00000748602274 (((10^274+10^137+1)*(2^452-3)/3+10^411*1972-1)/53366409470) will enable a N-1 proof that http://factorization.ath.cx/index.ph...00000748438030 ((10^274+10^137+1)*(2^452-3)/3+10^411*1972) is prime.

Chris

[chris2be8]

After adding algebraic factors to http://factorization.ath.cx/index.ph...00000504241133 ((6607^853-1)/6606) I found that proving http://factorization.ath.cx/index.ph...00000755048276 (a 1067 digit PRP) will probably be enough to prove it prime.

Chris

[chris2be8]

Thanks for proving that.

Here's another:
Proving http://factorization.ath.cx/index.ph...00000755346596 is prime should enable a N-1 proof for http://factorization.ath.cx/index.ph...00000439186935 ((4122^937-1)/4121).

Chris

[chris2be8]

And another:

Proving http://factorization.ath.cx/index.ph...00000755505371 should be enough to prove http://factorization.ath.cx/index.ph...00000512390486 ((3581^967-1)/3580) is prime.

Chris

[chris2be8]

And ...

Proving http://factorization.ath.cx/index.ph...00000756068010 will enable a N-1 proof for http://factorization.ath.cx/index.ph...00000439186901 ((4854^1009-1)/4853).

Chris

[chris2be8]

And proving http://factorization.ath.cx/index.ph...00000759078678 should be enough to prove http://factorization.ath.cx/index.ph...00000439186888 ((4735^1153-1)/4734) is prime. The former is 452 digits and the latter is 4234 digits so it's a bigger ration than usual.

Chris

[chris2be8]

Another:

Proving http://factorization.ath.cx/index.ph...00000759995166 is probably enough to prove http://factorization.ath.cx/index.ph...00000696698412 ((116^2089+1)/117) is prime.

Chris

[chris2be8]

And another:

Proving http://factorization.ath.cx/index.ph...00000759997087 will enable a N-1 proof that http://factorization.ath.cx/index.ph...00000296002061 (22^3217+21) is prime (at least this one is certainly large enough for the proof).

Chris

[axn]

Originally Posted by chris2be8

Another:

Proving http://factorization.ath.cx/index.ph...00000759995166 is probably enough to prove http://factorization.ath.cx/index.ph...00000696698412 ((116^2089+1)/117) is prime.

Chris

It wasn't. However, adding some more missing algebraic factors did the trick.

[chris2be8]

Originally Posted by chris2be8

Another:

Proving http://factorization.ath.cx/index.ph...00000759995166 is probably enough to prove http://factorization.ath.cx/index.ph...00000696698412 ((116^2089+1)/117) is prime.

Chris

That wasn't quite enough. So I started work on the smallest factor of N-1, (116^116+1)/5549418630282309787479951401753137, and found:

********** Factor found in step 2: 1563721650332372051297386247663898037313
Found probable prime factor of 40 digits: 1563721650332372051297386247663898037313
Probable prime cofactor 34571626573845918564783429269016198081709009231700089277835355381228515794200673865236406976328168287033463361692761363974121183975856856744607152825112929989944807057 has 167 digits

Which was enough to prove (116^2089+1)/117 is prime.

Chris

Edit. I didn't notice AXN's post before I made this one. But I added the factors above to factordb a couple of hours ago but factordb took a while to run the N-1 test.

@AXN, what algebraic factors did you add? I thought I'd added all possible ones before I asked for the smal PRP to be proved.

Edit 2: Is anyone working on the PRP in post 204?

[axn]

Originally Posted by chris2be8

@AXN, what algebraic factors did you add? I thought I'd added all possible ones before I asked for the smal PRP to be proved.

Hmmm... I was just working thru the algebraic factors from bottom up and supplying factors and all of a sudden one of the top level composites got factored. So I took credit for it. Must've been the factor you submitted.