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Old Feb 8, 2013, 04:56 PM   #1
Doctor Q
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For all you math geeks: we've got a new Mersenne prime!

GIMPS, the Great Internet Mersenne Prime Search, reports:
On January 25th, prolific GIMPS contributor Dr. Curtis Cooper discovered the 48th known Mersenne prime, 2^57,885,161 - 1, a 17,425,170 digit number.

This find shatters the previous record prime number of 12,978,189 digits, also a GIMPS prime, discovered over 4 years ago. The discovery is eligible for a $3,000 GIMPS research discovery award.
So take that, 12978189-digit Mersenne prime. Your reign is over!

A text file with all of the digits of this new prime number would be over 22MB in size! But it makes wonderful bedtime reading.

I find it amusing that they say that the 47th Mersenne prime was discovered over 4 years ago. According to their own logs it was April 12, 2009, which makes it 3.79 years ago. I guess arithmetic was never their strong suit.
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Old Feb 8, 2013, 05:33 PM   #2
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Yep, there's a reason I was a Philosophy major....

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Old Feb 8, 2013, 05:56 PM   #3
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$3,000!!! And we thought we would never use math in real life.
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Old Feb 8, 2013, 06:47 PM   #4
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Originally Posted by Mac'nCheese View Post
$3,000!!! And we thought we would never use math in real life.
I was hoping the payment amount was itself a Mersenne prime, or at least a prime.
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Old Feb 9, 2013, 07:38 AM   #5
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Quote:
Originally Posted by LPZ View Post
How many of those 17,425,170 digits were zeros?

OK, here's any easier one. Write the prime in binary instead of decimal. How many zeros now?
Quote:
Originally Posted by Doctor Q View Post
I just counted, and found that it begins with an infinite number of leading zeros!
just in case someone still want to know ...

0: 1'739'652
1: 1'743'497
2: 1'739'844
3: 1'745'602
4: 1'743'528
5: 1'739'641
6: 1'742'677
7: 1'743'436
8: 1'743'298
9: 1'743'995

standard deviation rough 2'076
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Old Feb 9, 2013, 08:40 AM   #6
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Quote:
Originally Posted by christianjapan View Post
just in case someone still want to know ...

0: 1'739'652
1: 1'743'497
2: 1'739'844
3: 1'745'602
4: 1'743'528
5: 1'739'641
6: 1'742'677
7: 1'743'436
8: 1'743'298
9: 1'743'995

standard deviation rough 2'076
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ID:	395641
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Old Feb 8, 2013, 05:57 PM   #7
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Quote:
Originally Posted by Doctor Q View Post
GIMPS, the Great Internet Mersenne Prime Search, reports:[indent][i]On January 25th, prolific GIMPS contributor Dr. Curtis Cooper discovered the 48th known Mersenne prime, 2^57,885,161 - 1, a 17,425,170 digit number.
How many of those 17,425,170 digits were zeros?

OK, here's any easier one. Write the prime in binary instead of decimal. How many zeros now?
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Old Feb 8, 2013, 06:01 PM   #8
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Originally Posted by LPZ View Post
How many of those 17,425,170 digits were zeros?
I just counted, and found that it begins with an infinite number of leading zeros!
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Old Feb 8, 2013, 06:02 PM   #9
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Man, did I ever stumble on the wrong thread!!!

Advanced math for me is balancing my checkbook!!!

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Old Feb 8, 2013, 06:19 PM   #10
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It's a very easy number to write in binary as this video demonstrates.

Warning to Doctor Q... if you haven't heard of this YouTube channel, it may consume a lot of your time!



----------

Quote:
Originally Posted by LPZ View Post
OK, here's any easier one. Write the prime in binary instead of decimal. How many zeros now?
None!
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Old Feb 9, 2013, 10:16 AM   #11
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Quote:
Originally Posted by Doctor Q View Post
GIMPS, the Great Internet Mersenne Prime Search, reports:
On January 25th, prolific GIMPS contributor Dr. Curtis Cooper discovered the 48th known Mersenne prime, 2^57,885,161 - 1, a 17,425,170 digit number.

This find shatters the previous record prime number of 12,978,189 digits, also a GIMPS prime, discovered over 4 years ago. The discovery is eligible for a $3,000 GIMPS research discovery award.
So take that, 12978189-digit Mersenne prime. Your reign is over!

A text file with all of the digits of this new prime number would be over 22MB in size! But it makes wonderful bedtime reading.

I find it amusing that they say that the 47th Mersenne prime was discovered over 4 years ago. According to their own logs it was April 12, 2009, which makes it 3.79 years ago. I guess arithmetic was never their strong suit.

I took one look at that and thought, I'm with Barbie on this one.

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Old Feb 9, 2013, 01:00 PM   #12
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If you concatenate all known primes, what is the distribution of digits?

Edit: I'll (partially) answer my own question using the first 50,000,000 prime numbers.
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Old Feb 9, 2013, 04:20 PM   #13
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About graphical presentations of data? -- that's Edward Tufte land.

http://www.edwardtufte.com/tufte/index

No one better, or more interesting, in my opinion.
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Old Feb 9, 2013, 04:52 PM   #14
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Quote:
Originally Posted by mobilehaathi View Post
If you concatenate all known primes, what is the distribution of digits?

Edit: I'll (partially) answer my own question using the first 50,000,000 prime numbers.
Well, they can't end in 0, 2, 4, 5, 6 or 8. That might be reflected in your plot.
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Old Feb 9, 2013, 04:58 PM   #15
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Here is something you might find interesting. Here I've divided the first 50,000,000 primes into bins of 1,000,000 and calculated the frequency with which the digit 0 occurred across all numbers in a bin.

The spikes that start at bin 12 coincide with bins that contain prime numbers that differ in the 100,000,000's digit. For example the first prime in bin 12 is 198,491,329 and the last is 217,645,177. The 100,000,000's digit turns over, we start to see a lot of primes in the low 200,000,000's, and we get a spike because of all the new 0's showing up. I bet there is also something to say (implied by this data) about the distribution of primes along the number line between 100,000,000 and 999,999,999.

The other digits have similarly curious patterns, but I don't have a good explanation for those yet. (Edit: Actually I do, its just the bins surrounding the number with the most of that particular digit in it)







Quote:
Originally Posted by LPZ View Post
Well, they can't end in 0, 2, 4, 5, 6 or 8. That might be reflected in your plot.
Certainly is!
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Old Feb 9, 2013, 07:42 PM   #16
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I went to school in the U.S.. Math is an afterthought here.
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Old Feb 10, 2013, 04:35 AM   #17
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I went to school in the U.S.. Math is an afterthought here.
That's very different from the UK. Here, Math is an incorrect spelling. Maths is an afterthought
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Old Feb 10, 2013, 04:54 AM   #18
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Originally Posted by mobilehaathi View Post
If you concatenate all known primes, what is the distribution of digits?

Edit: I'll (partially) answer my own question using the first 50,000,000 prime numbers.
1. Digits 1, 3, 7, 9 occur much more often because all primes end in these four digits (except 2 and 5).

2. Digit 0 is more rare because no prime starts with the digit zero.

3. Your table covers primes up to around 1.038 billion. The last 1.8 million primes all start with 1, that will make the digit 1 very slightly more common. If you had checked the primes up to 2 billion, the effect would have been quite strong.

4. Prime numbers get more rare as numbers get larger, which makes the larger digits less common as the first digit of a prime. That is just about visible in your chart.
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Old Feb 10, 2013, 08:18 AM   #19
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On a related side note: found a nice application called Rstudio which also is available as web server.

Quick setup a virtual dedicated Ubuntu Server and installed R and Rstudio; now I have R on my iPad with Xeon power at the backend.

Click image for larger version

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Ah, and purchased a Kindle book to read and learn about R. In the company we used in the last Lean SixSigma Training MiniTab; but R talks more to my programmer heart.
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Old Feb 10, 2013, 11:06 AM   #20
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Originally Posted by gnasher729 View Post
3. Your table covers primes up to around 1.038 billion. The last 1.8 million primes all start with 1, that will make the digit 1 very slightly more common. If you had checked the primes up to 2 billion, the effect would have been quite strong.
The 50,000,000th prime is 982,451,653, so this effect isn't there.

Quote:
4. Prime numbers get more rare as numbers get larger, which makes the larger digits less common as the first digit of a prime. That is just about visible in your chart.
Indeed, I'm aware that they get rarer, although I wasn't familiar with the rate at which they got rarer. The figure below plots the range of each bin, which we can use as a proxy measurement of scarcity (have to widen the bin to catch the same number of primes). A better measurement would, obviously, be a count of the number of primes within a fixed window along the number line, but I'm lazy and I thought this was interesting too.
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The true way is along a rope that is not spanned high in the air, but only just above the ground. It seems intended more to cause stumbling than to be walked along.
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Old Feb 12, 2013, 08:09 AM   #21
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Originally Posted by Doctor Q View Post
the 48th known Mersenne prime, 2^57,885,161 - 1, a 17,425,170 digit number....
A text file with all of the digits of this new prime number would be over 22MB in size! But it makes wonderful bedtime reading.
I find it amusing that you say that. A text file to hold a 17,425,170 digit number would be oh, say about 17,425,171 bytes long give or take a few bytes. From where did you pull your silly little number? Even more interesting is that you could compress this file below 100 bytes including the program to reexpand it without too much trouble.

Quote:
I find it amusing that they say that the 47th Mersenne prime was discovered over 4 years ago. According to their own logs it was April 12, 2009, which makes it 3.79 years ago. I guess arithmetic was never their strong suit.
Pot, meet the kettle. I guess arithmetic is not your strong suit either.
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Old Feb 12, 2013, 08:47 AM   #22
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I find it amusing that you say that. A text file to hold a 17,425,170 digit number would be oh, say about 17,425,171 bytes long give or take a few bytes. From where did you pull your silly little number?
And how large would the text file be if commas were used as separators every three digits?
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Old Feb 12, 2013, 08:52 AM   #23
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I find it amusing that you say that. A text file to hold a 17,425,170 digit number would be oh, say about 17,425,171 bytes long give or take a few bytes. From where did you pull your silly little number? Even more interesting is that you could compress this file below 100 bytes including the program to reexpand it without too much trouble.
The number is a little over 22MB because of commas. You end up with 23 million some characters then divide by 1024. The number was likely pulled from the web sites reporting it as being over 22MB because the main file that is out there holding this prime number contains the commas. While your comment is accurate, so is Doctor Q's.

Also, do you have a source that shows you could compress this under 100 bytes along with the program to reexpand it? I'm not asking as a challenge. I'm a programmer and genuinely curious.
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Old Feb 12, 2013, 09:13 AM   #24
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Even more interesting is that you could compress this file below 100 bytes including the program to reexpand it without too much trouble.
Now I'm interessted; how you can compress 17m digits in less the 100 bytes; and get it back ? typo ?
Something like Huffman with binary tree would not help; the distribution of members is equal; the tree would be balanced hence no advantage due to different entropies ...
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Old Feb 12, 2013, 09:24 AM   #25
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Now I'm interessted; how you can compress 17m digits in less the 100 bytes; and get it back ? typo ?
Something like Huffman with binary tree would not help; the distribution of members is equal; the tree would be balanced hence no advantage due to different entropies ...
Yeah that's what I was looking at. Even if you went into double or triple digit numbers I doubt there would be enough repetition to bother storing them in the table. Coding just the single digits doesn't reduce your bits enough on average. I have the file downloaded and have removed all non-digit characters. I compressed it with 7-zip's ultra compression (not that it is optimized for a random distribution of digits at all) and got it to 7,667,712 bytes. 7.6 is a little under half of the 17 million bytes which makes sense. Not sure how to get rid of the other 7,667,612+ bytes to get it under 100 bytes (need room for the decompressor).
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