Thread for posting tiny primes

[CRGreathouse]

Originally Posted by 3.14159

Any random prime integer.

OK, but what's random and how can you tell?

In particular, I'd like to make a submission and I'd like to know if you'll allow it before spending too much effort. (A large majority of the times I've submitted something for inclusion on one of your lists, you've changed the rules to disallow it.)

Originally Posted by 3.14159

I disallow: Mersennes and Fermats, because they have special-form factors.

My number is not of the form 2^n - 1, nor is it of the form 2^(2^n) + 1.

[3.14159]

Originally Posted by Charles

In particular, I'd like to make a submission and I'd like to know if you'll allow it before spending too much effort. (A large majority of the times I've submitted something for inclusion on one of your lists, you've changed the rules to disallow it.)

Because you use trickery! You always use trickery!

Also: For which item would you like to make a submission?

Originally Posted by Charles

My number is not of the form 2^n - 1, nor is it of the form 2^(2^n) + 1.

And it should not be of the form b^2[sup]n[/sup] + 1 (Generalized Fermat), either.

[3.14159]

Originally Posted by Charles

OK, but what's random and how can you tell?

Step 1. Pick a number.
Step 2. Trial division up to its square root.
Step 3. If prime, report here.

That is, if you are applying for the unofficial trial factoring proof.

[CRGreathouse]

Originally Posted by 3.14159

For which item would you like to make a submission?

Trial-division prime.

Originally Posted by 3.14159

And it should not be of the form b^2[sup]n[/sup] + 1 (Generalized Fermat), either.

It's not of that form. Is that good enough?

[3.14159]

Originally Posted by Charles

Trial-division prime.

Excellent.

Originally Posted by Charles

It's not of that form. Is that good enough?

I still think you have one last piece of trickery up your sleeves..

[CRGreathouse]

Originally Posted by 3.14159

Step 1. Pick a number.
Step 2. Trial division up to its square root.
Step 3. If prime, report here.

I've done step 1, but I'm not sure if you'll accept it. You've denied almost all of my previous attempts.

I'm working on #2. The number is large (though of course not as large as my Mersenne) so this step is hard.

[3.14159]

Originally Posted by Charles

I've done step 1, but I'm not sure if you'll accept it. You've denied almost all of my previous attempts.

They were Mersenne numbers. Trickery!

Originally Posted by Charles

I'm working on #2. The number is large (though of course not as large as my Mersenne) so this step is hard.

I'm guessing it's a p22-p24?

[CRGreathouse]

Mersenne primes and generalized Fermat primes are disallowed, but other numbers are good (provided, of course, that you actually do the trial division up to the square root).

[3.14159]

The largest number I have tried thus far is 8905881751755136749253, a general p22.

Originally Posted by Charles

Fermat primes and generalized Fermat primes are disallowed, but other numbers are good (provided, of course, that you actually do the trial division up to the square root).

Cough, Mersenne numbers (2^p -1) are disallowed.

[CRGreathouse]

Originally Posted by 3.14159

They were Mersenne numbers. Trickery!

Mersenne numbers were allowed at the time that I posted them.

Originally Posted by 3.14159

I'm guessing it's a p22-p24?

No. It's either <= 9999999999999999999973 or >= 100000000000000000000117.

[3.14159]

Originally Posted by Charles

No.

p25-p27?