The Chess Variant Forum
General Category => Variant Theory => Topic started by: chilipepper on January 10, 2018, 12:33:57 am

This doesn't have much to do with chess (although the huygens chess piece jumps prime numbers of squares), but I just heard that a new and the largest prime number has been discovered (December 2017). It is:
2^(77,232,917) − 1
It has more than 23 million digits, and is creating big chatter in the math world!
One source is here (and plenty others can be found easily):
https://www.mersenne.org/primes/press/M77232917.html
Stunnning and unbelievable news (at least to math nerds)!!! ::)

That's pretty big. The best I ever did was to discover the 84th largest prime number ever, back on June 28, 2013.
Mine was 70000000000000000...00000000000001 with 902707 zeroes.
https://primes.utm.edu/bios/page.php?id=3011

Really? I didn't know there were any large primes one away from a poweroften number (not sure if I said that right)...A number with almost all zeros.
Maybe there's actually plenty of them (not sure)? Although I'm sure all large primes are hard to find. Did you find it with GIMPS, or some other method?
It's pretty amazing  good work! :)

Really? I didn't know there were any large primes one away from a poweroften number (not sure if I said that right)...A number with almost all zeros.
Maybe there's actually plenty of them (not sure)? Although I'm sure all large primes are hard to find. Did you find it with GIMPS, or some other method?
It's pretty amazing  good work! :)
Thanks. I found a bunch of large primes of that form. I was "showing off" with my 5.0 GHz supercomputers I had access to. Just to prove they weren't "flukes" I found two prime numbers with each coefficient.
And no, I was not a part of GIMPS, this was a solo effort.
7 x 10 raised to the ridiculous + 1 has two different primes
6 x 10 raised to the ridiculous + 1 has two different primes
I even used 2 raised to the power of 64  189 as a coefficient. I proved, separately, that 2^64  189 is the largest prime number less than 2^64 that can be used as a coefficient for a 10^n + 1 sequence and still generate a prime number.
[attachimg=1]

That's pretty awesome stuff  especially that you did the math and programming yourself (not just running GIMPS on your home PC).
Some people don't think prime numbers are useful for anything. But I believe NASA or other astronomers have sent prime numbers into outerspace. It's a way to announce to extraterrestrials that there's intelligent life here on earth. So, maybe some green creature will be visiting your home sometime. Better you than me. :P
Btw, what is the "799167/" in the 6th entry? Is that the first six digits of the very long coefficient? That prime is interesting because even in its collapsed form it still requires a lengthy expression.

That's pretty awesome stuff  especially that you did the math and programming yourself (not just running GIMPS on your home PC).
Btw, what is the "799167/" in the 6th entry? Is that the first six digits of the very long coefficient? That prime is interesting because even in its collapsed form it still requires a lengthy expression.
Yeah that was another "show off" thing I did. The coefficient is so large, it could not fit on one line. So I generated a large Payam Number for Base2, and generated a power of 2 prime using 799167535... as the coefficient. Basically is was 2 raised to the power of 1.2 million, times that large coefficient, minus 1. I think it's the largest coefficient ever used to calculate a prime.
Payam Numbers are explained here: http://mathworld.wolfram.com/PayamNumber.html
That's why I did that stuff. I still own the record for the prime containing the greatest number of zeroes. If you think about it, the number is "mostly nothing."
:)
By the way, GIMPS stands for the Great Internet Mersenne Prime Search. That only works for 2^n  1 = prime. None of my numbers take that form, so therefore, I could not have been using GIMPS.

Really? I didn't know there were any large primes one away from a poweroften number (not sure if I said that right)...A number with almost all zeros.
701
7001
70001
700001
In fact, every prime number is 1 away from a multiple of 6. So every prime number can be represented by (6 * k) +/ 1 for some value of k.

Here is the huygens, which is a chess piece that jumps prime numbers of squares (orthogonal directions). It was named after Christiaan Huygens, a Dutch mathematician and astronomer. (Other things have been named after him too, including a spacecraft that visited Saturn).
[attach=1]
By being the discoverer of several prime numbers, you have helped to determine the specific moves of the huygens. For example, the huygens can make a jump of [6x10^(231617) + 1] squares. The huygens is played best in versions of infinite chess (unbounded boards), and obviously would not be very interesting on the normal 8x8 board.
I'm not sure if this move would actually ever be useful in a chess game, but thanks to your work, at least we understand the huygen's moves a little better. :)