Share N+/-1 Primality Proofs

[schickel]

Originally Posted by wblipp

Although I don't know why there is interest in (3^3333+4), I enjoy finding cases like (3^3333+4)/31 in the PRP lists, where I can visually spot that N-1 has a difference of powers of 3 (3^3333-3^3) that leaves the cyclotomic number (3^3330-1). In many cases, including this one, helping the factordb find the algebraic factors of the cyclotomic number completes the primality proof.

While I can't speak on the worth of a particular number, I can point out a project that worked on numbers with forms like this that had some considerable effort behind it. It looks like WsF never revived the project, but I was reminded of it by some work I had done that was sitting around in my files.....

[wblipp]

Originally Posted by schickel

I can point out a project that worked on numbers with forms like this

It looks like the project has been inactive for a few years. If it were still active, it would be nice to have them update the factordb with their factors and primality proofs.

Browsing some some larger PRPs, I quickly found another one of these today. The proof was easily completed by helping the factordb find the algebraic factors of N+1. 14^2080+13

[lorgix]

I have helped many proofs like this.

I'm really hoping the database will get better at recognizing algebraic factors.

[YuL]

A very easy one: (5^3168-1)*85/24+1, N-1 needed some factors from 5^3168-1.

[YuL]

The same for (10^798-1)*970/99+1: N-1 needed help from 10^798-1
and (5^1428-1)*85/24+1: N-1 needed help from 5^1428-1
(2^3023+27)/5: N+1 needed help from 2^3018+1
(16^564-1)*176/85+1: N-1 needed help from 2^2256-1

[YuL]

(2^5354*75+1)/7: uploading a primality certificate for ((2^5354*75+1)/7-1)/3018 allowed an N-1 proof.

[henryzz]

Would it be possible to download all the prps with form (b^n+c)/d and similar forms? It should be possible to parse that sort of expression in a script such that the necessary factors of plus or minus one can be supplied.

[henryzz]

(10^1612*7-9)/691 N-1 needed help from 10^1610-1

[wblipp]

(10^1872*58+41)/99 needed help from 10^1872-1

[lorgix]

8863^433-1 needed help with the factors of 8863^432-1.

There are many such numbers.

[henryzz]

Once you have a list of the numbers the numbers of the form (b^n*k+-c)/d will be recognized by this in notepad++
^\(([0-9]+)\^([0-9]+)\*([0-9]+)([+-])([0-9]+)\)/([0-9]+)
I replaced these by:
correct (\1^\2*\3\4\5)/\6
Then I sort the lines in the file and remove those without correct at the beginning. Then I remove correct from the beggining of the lines.

Now I have a list of numbers which can be parsed and manipulated by a simple program.

Unfortunately show as plain text only works for composites so I can only manually copy 1000 at once and can't use a script to pull them. I have attached the results of the current first 1000 for people to browse more easily
A program finding which are possible should follow shortly.