[QUOTE=Charles]I have now proved the primality of 618970019642690137449562111, a p27, with trial division. This was the hardest proof by trial division I had ever attempted.
[/QUOTE]

Please, tell me, exactly how did your computer's speed increase [B]exponentially[/B]?

If it took me about 10-15 minutes to prove a p22 prime; It should have taken you a similar timeframe to prove the same number prime; A number ≈70000-75000 times that size should have taken many thousands of times longer.

Or did you get started 3-6 months ago?

[QUOTE=3.14159;228575]Please, tell me, exactly how did your computer's speed increase [B]exponentially[/B]?[/QUOTE]

You should look closer here. That's what I meant!

618970019642690137449562111 = 2^89-1 and therfore only factors = 2kp+1 have to be considered and tested!

[QUOTE=Karsten]618970019642690137449562111 = 2^89-1 and therfore only factors = 2kp+1 have to be considered and tested!
[/QUOTE]

Mersenne number? Cheating not allowed, :smile:

[B]General numbers only. [/B] Optionally, Proth numbers. Take a probable prime and prove it prime, using trial-factoring only.

So, Charles, try again, with a general or Proth number. (Can either be b = 2 or regular). Unless your computer speeds up by 10000 on demand, let's see how that works out.

[QUOTE=3.14159;228577]Mersenne number? Cheating not allowed[/QUOTE]

Really... did you think I'd enter into one of these without some sort of trick?

[QUOTE=Charles]Really... did you think I'd enter into one of these without some sort of trick?
[/QUOTE]

The first was composite, divisible by 7, and the next is a Mersenne number.

You so far have contributed nothing. Next!

Reporting for 17 or 18: (981248619155265231198804096876768467232996282812538785080944608471724730019235498676*3000!+1)/486830979235504387397288386896757349991446828735164830762828213017832532827952201 is prime, 9051 digits.

This may probably be in Special Cofactor.

[QUOTE=3.14159;228581]The first was composite, divisible by 7, and the next is a Mersenne number.

You so far have contributed nothing. Next![/QUOTE]

the one thing i see you contributing to most is a headache by changing rules so much.

[QUOTE=science_man_88]the one thing i see you contributing to most is a headache by changing rules so much.
[/QUOTE]

I'm merely keeping trickeries out of the list.

[QUOTE=3.14159;228581]The first was composite, divisible by 7[/QUOTE]

Copy/paste error. I fixed it before you posted, but you quoted the unedited version.

[QUOTE=science_man_88;228583]the one thing i see you contributing to most is a headache by changing rules so much.[/QUOTE]

+1. If I had a nickel for every time he did that... well, I'd have about a buck. But still, that's a lot of rules changes.

[QUOTE=CRGreathouse;228589]+1. If I had a nickel for every time he did that... well, I'd have about a buck. But still, that's a lot of rules changes.[/QUOTE]

And it's a ridiculous point of his list:

1. Wasting CPU-cycles to find the biggest prime proven by trial division.
2. He can't recognize simple 'easy' numbers.
3. He can't prove if such number is proven only by trial division.