DIR Return Create A Forum - Home
---------------------------------------------------------
The Chess Variant Forum
HTML https://chessvariantforum.createaforum.com
---------------------------------------------------------
*****************************************************
DIR Return to: Variant Theory
*****************************************************
#Post#: 38--------------------------------------------------
A new and largest-known prime number has been discovered!
By: chilipepper Date: January 9, 2018, 11:33 pm
---------------------------------------------------------
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):
HTML https://www.mersenne.org/primes/press/M77232917.html
Stunnning and unbelievable news (at least to math nerds)!!! ::)
#Post#: 40--------------------------------------------------
Re: A new and largest-known prime number has been discovered!
By: GothicChessInventor Date: January 10, 2018, 8:25 pm
---------------------------------------------------------
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.
HTML https://primes.utm.edu/bios/page.php?id=3011
#Post#: 41--------------------------------------------------
Re: A new and largest-known prime number has been discovered!
By: chilipepper Date: January 10, 2018, 9:52 pm
---------------------------------------------------------
Really? I didn't know there were any large primes one away from
a power-of-ten 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! :)
#Post#: 42--------------------------------------------------
Re: A new and largest-known prime number has been discovered!
By: GothicChessInventor Date: January 11, 2018, 12:06 pm
---------------------------------------------------------
[quote author=chilipepper link=topic=18.msg41#msg41
date=1515642760]
Really? I didn't know there were any large primes one away from
a power-of-ten 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! :)
[/quote]
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]
#Post#: 48--------------------------------------------------
Re: A new and largest-known prime number has been discovered!
By: chilipepper Date: January 11, 2018, 4:49 pm
---------------------------------------------------------
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 outer-space. It's a way to announce to extra-terrestrials
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.
#Post#: 50--------------------------------------------------
Re: A new and largest-known prime number has been discovered!
By: GothicChessInventor Date: January 12, 2018, 8:35 am
---------------------------------------------------------
[quote author=chilipepper link=topic=18.msg48#msg48
date=1515710992]
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.
[/quote]
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 Base-2, 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:
HTML 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.
#Post#: 51--------------------------------------------------
Re: A new and largest-known prime number has been discovered!
By: GothicChessInventor Date: January 12, 2018, 9:57 am
---------------------------------------------------------
[quote author=chilipepper link=topic=18.msg41#msg41
date=1515642760]
Really? I didn't know there were any large primes one away from
a power-of-ten number (not sure if I said that right)...A number
with almost all zeros.
[/quote]
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.
#Post#: 54--------------------------------------------------
Re: A new and largest-known prime number has been discovered!
By: chilipepper Date: January 12, 2018, 7:36 pm
---------------------------------------------------------
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. :)
*****************************************************