Largest known prime

2^24036583 - 1 (which has over 7 million digits)

http://www.utm.edu/research/primes/largest.html

There's this thing, it's called a "search engine."

Sorry for the apparent lack of a connection to any game, but this is a response to an off-topic post.

Tim could also have tried the Mersenne page link on my maths page. ;-)

There's this thing, called "I learn new things every day."

Fellow players, having David, Tasmanian Devil, and Klaashaas stationing with us at LG, we have nothing to worry about any more. They will answer any marginally-not-so-silly questions we may raise, and yet will feed us riddles and puzzles that will make us scratch off all our hair.

Go ahead. Ask, and you shall receive. :)

I do not know if this counts as a marginally not so silly question or only as a silly question.

In which part of the world did chess have its birth? Hee hee ;-)

Cannot believe that there is a time when I can be in the position of giving answers.

To the best of my knowledge, Chess originated in Arabian peninsula. It propagated to Europe, and has become Chess today. It did China, and has become Chinese Chess today. It did Japan, and has become Japanese Chess today.

A+, yes? :)

There is a historic theory, that chess has it's origins in India as a board game. Then the game went to China as a board game and in Mongolia they changed the stones to leather plates and spread it over big parts of Asia and Europe. As usual, there is some evidence and further research must be done ... ;)

Well, now that we mentioned Mersenne, it is not fair to mention Fermat also to continue our trivial pursuits.

Like many of us Go, Hex, and chess players, Fermat was not a pro. He was merely an amateur mathematician. What was his true profession? :)

Lawyer !

Bravo, Michael, you received one point.

OK, this is a 2-point trivial-pursuit question:

Why is 26 so unique? :)

Since primes have been mentioned, are you thinking of the famous polynomial in 26 variables whose positive values are all primes? That 26 is not unique.

the one number which is right in between a square and a cube ... did i ever mention i was into maths tim? :P

special numbers...once i was in a taxi, it's number was 1729, any idea what's so special about that?

That one I do know...the smallest integer that is the sum of two cubes in two different ways (of course, all mathematicians know the story with Ramanujan and Hardy).

("M45") 2^43,112,609-1, a mammoth 12,978,189 digit number, found on a University of California Los Angeles (UCLA) computer in the GIMPS PrimeNet network

I assume from "M45" that it's a Mersenne prime. What is it about the Mersenne numbers that makes them easier to test for primality?

I could not resist...

It is linked with Fibonacci numbers, Lucas sequence and :

Lucas-Lehmer Test (1930): Let n be an odd prime. The Mersenne number M(n) = 2^n-1 is prime if and only if S(n-2) = 0 (mod M(n)) where S(0) = 4 and S(k+1) = S(k)^2-2.

There are two families or proven primes, those were n-1 factorization is known (Pepin's test) and those like Mersenne where n+1 factorization is known.

You can find more here

Anything with a sufficiently large factorisation of P+1 or P-1 is easy to test for primality. Mersenne numbers have the benefit of having the modular reduction stage of the multiplications (squarings) happen not just "for free", but also with the benefit of halving your FFT sizes. If anything, Generalised Ferman Numbers have all the same benefits, but the code's simpler, so if optimised to the same degree should be fractionally faster.