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 >>
50th Mersenne Prime found!
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50th Mersenne Prime found!
Art Neuendorffer
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Re: 50th Mersenne Prime found!
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?
Bruce
Have any large base systems been developed?
Bruce
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Re: 50th Mersenne Prime found!
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?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.
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!
Being able to accurately express something in a much more efficient manner has value. Using less paper is good.Chris Peterson wrote: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?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.
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.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.
Very good to know. Thanks.(The ancient Babylonians utilized base 60, sexagesimal. AFAIK that's the largest base ever used for common math.)
Bruce
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Re: 50th Mersenne Prime found!
15(base 10) = F(base 60) too.
There are lots of base conversion tools available online -- if you really have nothing else to do.
![Wink ;-)](./images/smilies/icon_wink.gif)
Rob
There are lots of base conversion tools available online -- if you really have nothing else to do.
![Shocked :shock:](./images/smilies/icon_eek.gif)
![Wink ;-)](./images/smilies/icon_wink.gif)
Rob
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Re: 50th Mersenne Prime found!
And yet, that's precisely how it was found. Binary computation. Internal binary representation. (Computers don't use hexadecimal.)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.
Chris
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Re: 50th Mersenne Prime found!
BDanielMayfield wrote:
The 50th Mersenne Prime would require a staggering number of digits in binary.
- 77,232,917 bits to be precise:
but, at least, it would be easy to remember (so long as you were allowed to count on your fingers).
Art Neuendorffer
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Re: 50th Mersenne Prime found!
Bit. As in binary digit.neufer wrote:BDanielMayfield wrote: The 50th Mersenne Prime would require a staggering number of digits in binary.
- 77,232,917 bits to be precise:
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51th Mersenne Prime found!
https://en.wikipedia.org/wiki/Largest_known_prime_number wrote:
<<The largest known prime number (as of January 2020) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. Its value is:
148894445742041325547806458472397916603026273992795324185271289425213239361064475310309971132180337174752834401423587560... (24,861,808 digits omitted)
...062107557947958297531595208807192693676521782184472526640076912114355308311969487633766457823695074037951210325217902591.>>
Art Neuendorffer
Re: 51th Mersenne Prime found!
That's a funny shape of that curve. Reminds me somehow of the Universe with expands faster or slower during different epochs.neufer wrote: ↑Fri Jul 31, 2020 6:26 pmhttps://en.wikipedia.org/wiki/Largest_known_prime_number wrote:
<<The largest known prime number (as of January 2020) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. Its value is:
148894445742041325547806458472397916603026273992795324185271289425213239361064475310309971132180337174752834401423587560... (24,861,808 digits omitted)
...062107557947958297531595208807192693676521782184472526640076912114355308311969487633766457823695074037951210325217902591.>>
Although, unlike the Universe, the prime number curve seems to be slowing down.
Ann
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Re: 51th Mersenne Prime found!
Careful... the y-axis is logarithmic. The declining slope of the curve only indicates "slowing down" in certain contexts.Ann wrote: ↑Fri Jul 31, 2020 7:42 pmThat's a funny shape of that curve. Reminds me somehow of the Universe with expands faster or slower during different epochs.neufer wrote: ↑Fri Jul 31, 2020 6:26 pmhttps://en.wikipedia.org/wiki/Largest_known_prime_number wrote:
<<The largest known prime number (as of January 2020) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. Its value is:
148894445742041325547806458472397916603026273992795324185271289425213239361064475310309971132180337174752834401423587560... (24,861,808 digits omitted)
...062107557947958297531595208807192693676521782184472526640076912114355308311969487633766457823695074037951210325217902591.>>
Although, unlike the Universe, the prime number curve seems to be slowing down.
Ann
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Flattening the Curve
Right Chris. It would become a favorite tool of flat Earth type thinkers, if they could grasp the concept. Most any curve can be flattened simply by switching to a log or semi-log graph.Chris Peterson wrote: ↑Fri Jul 31, 2020 7:54 pmCareful... the y-axis is logarithmic. The declining slope of the curve only indicates "slowing down" in certain contexts.
Just as zero is not equal to infinity, everything coming from nothing is illogical.
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Re: 51th Mersenne Prime found!
The Universe had 2 kicks in the butt after the Big Bang:
- Inflation.
Dark Energy.
- Electronic computers ~1960
Massively parallel computers ~1985
Large scale distributed computing projects ~2000
![Question :?:](./images/smilies/icon_question.gif)
Perhaps (some subset of) the Mersenne prime exponents have some (as yet) undetermined regularity:
2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, 74207281, 77232917, 82589933, ...
(Blue color: proven consecutive Mersenne prime exponents.)
Art Neuendorffer