PARI's commands

[3.14159]

By decent-sized: The usual 1k-digit minimum, please. (750 for General Cofactor, and 1250 for Special Cofactor.)

[3.14159]

Originally Posted by science_man_88

yeah well if i was stupid I'd post 2^43112608*2^1+1 but you know this one already lol.

Mersenne numbers belong in General Cofactor, if you can prove that it is the cofactor of a number of the forms listed, following the new rules (Bold = My emphasis.)

Also: For verification: Post the factoring session data for General/Special cofactor.

[3.14159]

Also: If there have been distributed searches on k-b-b, can anyone point me to one, and what ranges were being searched? (This is to ensure I am not searching for what has already been searched for, like when I was searching for Generalized Fermats. Because they are already searched for up to 131072, up to 3 million, there is no point searching for them.)

I'm going to check to see the search ranges for Prime Sierpinski, since they search for items 2 or 5 (Base 5 Sierpinski project, if I remember correctly.)

[3.14159]

The k * 4549⁴⁵⁴⁹ range I am testing is rather barren.

k = 180k to 360k.

Nothing so far up to 270k.

Update: Nevermind: 265134 * 4549⁴⁵⁴⁹ + 1 is a PRP. Off to prove it prime. (Does Proth's theorem also apply to Generalized Proth numbers? Answered my own question: Not to odd-number bases)

Start: For n=4549 to 4549, For k=265134 to 265134 step 2, k*4549^n+1.
265134*4549^4549 + 1 may be prime. (a = 2)
265134*4549^4549 + 1 is prime! (verification : a = 3) [16646 digits]

[CRGreathouse]

Originally Posted by 3.14159

Factorwork must be done and the user cannot know one or more of the factors beforehand. The smallest factor can be no smaller than 7 digits.

How can you verify this? Factoring data can presumably be reconstructed if you know the factors.

[CRGreathouse]

Originally Posted by 3.14159

I already fixed your whining complaints.

I'd have to check, but I'd guess you fixed less than 25% of them. Of course this is not your fault -- I was intentionally not explicit about most of them. I don't care to be: my purpose is not to tell you what to do but to cause you to think more deeply.

Originally Posted by 3.14159

And, why would I be annoyed? All decent-sized primes of those 20 types are welcomed.

Only for the same reason you seemed to not like #969.

[science_man_88]

Originally Posted by 3.14159

Mersenne numbers belong in General Cofactor, if you can prove that it is the cofactor of a number of the forms listed, following the new rules (Bold = My emphasis.)

Also: For verification: Post the factoring session data for General/Special cofactor.

yeah I accidentally put +1 doh anyways if you keep changing the rules who cares not me.

[3.14159]

Originally Posted by CRGreathouse

How can you verify this? Factoring data can presumably be reconstructed if you know the factors.

You would have to go a long way to fake factor data. Meh, screw it. Too many people would take the time to fake everything.

To make sure it can't be faked: Smallest factor must at least be 65 digits and unknown to the user.

Yes, I'm sure someone would withhold it for 7-10 days and post it with fake data afterwards. Makes perfect sense.

Even better: Get rid of cofactor and replace it with complete factorization of a number of those forms.

[CRGreathouse]

Originally Posted by 3.14159

You would have to go a long way to fake factor data.

Maybe, maybe not. Perhaps I already have a program that fakes factor data.

Here's a Pari program that fakes trial division data

fake(p,q)={
  
};

That was easy. Faking rho data also seems doable. NFS seems hard to fake, I'll admit, but just because I don't know of a way doesn't mean it's impossible.

But my point, like my point about your obsolete category, is that this suggests that the category itself is a bad idea, not that this small group of people would be likely to deceive each other.

[3.14159]

Update: List is back down to 19 items. Restrictions still apply to the other items. I have gotten rid of cofactor and replaced it with completely factoring a number of the forms listed there. The smallest the number can be is 90 digits.

[CRGreathouse]

Originally Posted by 3.14159

To make sure it can't be faked: Smallest factor must at least be 65 digits and unknown to the user.

How can you verify that it was unknown to the user?

Originally Posted by 3.14159

Even better: Get rid of cofactor and replace it with complete factorization of a number of those forms.

That's fine -- but I still think we need a good way to judge the (prior) difficulty of finding a factorization.