50th Mersenne Prime found!

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neufer
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50th Mersenne Prime found!

Post by neufer » Tue Jan 09, 2018 10:42 pm

https://en.wikipedia.org/wiki/Largest_known_prime_number wrote:
<<As of January 2018, the largest known prime number is 277,232,917 − 1, a number with 23,249,425 digits. It was found in December 2017 by the Great Internet Mersenne Prime Search (GIMPS). A standard word processor layout (50 lines per page, 75 digits per line) would require 6,199 pages to display it. Its value is:

467333183359231099988335585561115521251321102817714495798582338593567923480521177207484311099740208849621368090038049317... (23,249,185 digits omitted) ...285376004518786055402223376672925679282131965467343395945397370476369279894627999939614659217371136582730618069762179071 >>
Art Neuendorffer

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Re: 50th Mersenne Prime found!

Post by BDanielMayfield » Wed Jan 10, 2018 4:21 am

Base 10 is just too insufficient for such enormous numbers. I looked into higher bases once when Art had made a similar post, but wasn't able to find anything higher than hexadecimal (base 16) in common use. What's called for is a much higher base system, say, base 100, in which there would be 100 characters to represent the base ten numbers 0 to 99. Such a system would be able to compress the exact expression of a humongously long real number into a more manageable size.

Have any large base systems been developed?

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Chris Peterson
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Re: 50th Mersenne Prime found!

Post by Chris Peterson » Wed Jan 10, 2018 4:50 am

BDanielMayfield wrote:What's called for is a much higher base system, say, base 100, in which there would be 100 characters to represent the base ten numbers 0 to 99. Such a system would be able to compress the exact expression of a humongously long real number into a more manageable size.
It would allow the number to be printed using less paper. I don't see what other value it would have. Would you or I have a better grasp of the number if it were notated in base 100?

No, going the other way is what makes the most sense. Expressing it in binary. Because once a number becomes to large to make any intuitive sense expressed in base 10, it's probably only being manipulated in a computer, anyway, and for that, base 2 is the natural system.

(The ancient Babylonians utilized base 60, sexagesimal. AFAIK that's the largest base ever used for common math.)
Chris

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Re: 50th Mersenne Prime found!

Post by BDanielMayfield » Wed Jan 10, 2018 6:04 am

Chris Peterson wrote:
BDanielMayfield wrote:What's called for is a much higher base system, say, base 100, in which there would be 100 characters to represent the base ten numbers 0 to 99. Such a system would be able to compress the exact expression of a humongously long real number into a more manageable size.
It would allow the number to be printed using less paper. I don't see what other value it would have. Would you or I have a better grasp of the number if it were notated in base 100?
Being able to accurately express something in a much more efficient manner has value. Using less paper is good.
No, going the other way is what makes the most sense. Expressing it in binary. Because once a number becomes to large to make any intuitive sense expressed in base 10, it's probably only being manipulated in a computer, anyway, and for that, base 2 is the natural system.
15(base 10) = F(base 16) = 1111(base 2), therefore hex is more efficient than the decimal and especially the binary systems, at least in character count. The 50th Mersenne Prime would require a staggering number of digits in binary.
(The ancient Babylonians utilized base 60, sexagesimal. AFAIK that's the largest base ever used for common math.)
Very good to know. Thanks.

Bruce
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rstevenson
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Re: 50th Mersenne Prime found!

Post by rstevenson » Wed Jan 10, 2018 2:48 pm

15(base 10) = F(base 60) too.

There are lots of base conversion tools available online -- if you really have nothing else to do. :shock: ;-)

Rob

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Re: 50th Mersenne Prime found!

Post by Chris Peterson » Wed Jan 10, 2018 2:49 pm

BDanielMayfield wrote:15(base 10) = F(base 16) = 1111(base 2), therefore hex is more efficient than the decimal and especially the binary systems, at least in character count. The 50th Mersenne Prime would require a staggering number of digits in binary.
And yet, that's precisely how it was found. Binary computation. Internal binary representation. (Computers don't use hexadecimal.)
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neufer
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Re: 50th Mersenne Prime found!

Post by neufer » Wed Jan 10, 2018 3:26 pm

BDanielMayfield wrote:
The 50th Mersenne Prime would require a staggering number of digits in binary.
  • 77,232,917 bits to be precise:
111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111... (77,232,677 bits omitted) ...111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

but, at least, it would be easy to remember (so long as you were allowed to count on your fingers).
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Re: 50th Mersenne Prime found!

Post by Chris Peterson » Wed Jan 10, 2018 3:31 pm

neufer wrote:
BDanielMayfield wrote: The 50th Mersenne Prime would require a staggering number of digits in binary.
  • 77,232,917 bits to be precise:
Bit. As in binary digit.
Chris

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