Share N+/-1 Primality Proofs

[MisterBitcoin]

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.

Good find!

[chris2be8]

Here are a few pairs where proving the first would enable a N+/-1 proof of the second:

1100000001301012630     ((7^400+1733)/82223086099553958-1)/4959216
1100000001297599962     (7^400+1733)/82223086099553958

1100000001301012779     ((7^400+2366)/65836284451077-1)/6510699610
1100000001299828044     (7^400+2366)/65836284451077

1100000001301704616     (2^3003-2^2992-2)/10
1100000001301704606     2^3003-2^2992-3

Chris

[chris2be8]

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.

For amusement value, (715^1531-1)/714 has an algebraic factor (715^85-1)/451315949140816371979283301682399702810216293018363947289071889906041442579144193134 which would be a fairly easy SNFS target if anyone wants to factor it.

Chris

[DukeBG]

Originally Posted by chris2be8

For amusement value, (715^1531-1)/714 has an algebraic factor (715^85-1)/451315949140816371979283301682399702810216293018363947289071889906041442579144193134 which would be a fairly easy SNFS target if anyone wants to factor it.

Chris

1531 doesn't divide 85, you probably meant 1530 as the exponent?

[axn]

Originally Posted by DukeBG

1531 doesn't divide 85, you probably meant 1530 as the exponent?

He meant, to prove (715^1531-1)/714, N-1 (i.e (715^1530-1)*715/714) has algebraic factor ...

[MDaniello]

Browsing the db i found this guy with a nice button to press next to "N+1".

I wonder how many of this cases, with N+/-1 already factored enough, are hidden in the db... probably too few to make looking for them worth the effort.

[MisterBitcoin]

Originally Posted by MDaniello

Browsing the db i found this guy with a nice button to press next to "N+1".

I wonder how many of this cases, with N+/-1 already factored enough, are hidden in the db... probably too few to make looking for them worth the effort.

Very lucky one. ^^

[GP2]

Originally Posted by MDaniello

I wonder how many of this cases, with N+/-1 already factored enough, are hidden in the db... probably too few to make looking for them worth the effort.

I remember finding one like this some months ago.

I was reviewing the list of PRP cofactors of Mersenne numbers and Wagstaff numbers in the low exponent ranges where Primo ECPP certificates were trivially obtained long ago, and for one of them there was now a button to press next to either N−1 or N+1, which hadn't been there earlier.

I believe it was for the PRP cofactor of M1361

[chris2be8]

Proving http://factordb.com/index.php?id=1100000001317157731 ((406^13*26^203+1)/27-1)/985790 will enable a N-1 proof that:
http://factordb.com/index.php?id=1100000001316295366 (406^13*26^203+1)/27 is prime.

Chris

[chris2be8]

Here are a pair of PRPs where proving the first would enable a N-1 proof the second is prime.

1100000001347839402     152089647^71-2      581
1100000001347858590     152089647^71*1686-3371     585

Chris

[MDaniello]

Does anybody knows what's the maximum number size factordb can deal with, as for N+/-1 proofs?
I found a really large PRP (>140k digits) suitable for a proof, but the server responded (not immediately) that the number was too big to prove.