For all you math geeks: we've got a new Mersenne prime!

[Doctor Q]

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.

[GermanyChris]

Yep, there's a reason I was a Philosophy major....

[Mac'nCheese]

$3,000!!! And we thought we would never use math in real life.

[LPZ]

Originally Posted by Doctor Q

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?

[Doctor Q]

Originally Posted by LPZ

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!

[Shrink]

Man, did I ever stumble on the wrong thread!!!

Advanced math for me is balancing my checkbook!!!

[SilentPanda]

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!



----------

Originally Posted by LPZ

OK, here's any easier one. Write the prime in binary instead of decimal. How many zeros now?

None!

[chown33]

Originally Posted by Mac'nCheese

$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.

[ChristianJapan]

Originally Posted by LPZ

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?

Originally Posted by Doctor Q

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

[SilentPanda]

Originally Posted by christianjapan

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

[ChristianJapan]

Originally Posted by SilentPanda

Attachment 395641

Yeah, i know. my presentation was poor. I always wanted some statistics package; now I installed R and even more clueless

[SilentPanda]

Originally Posted by ChristianJapan

Yeah, i know. my presentation was poor. I always wanted some statistics package; now I installed R and even more clueless

It's okay. I forgot to label what green means. So there's just a little dot off to the side...

[Happybunny]

Originally Posted by Doctor Q

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.

[mobilehaathi]

I suspect the NSA knew this one for a while now.

[Doctor Q]

Originally Posted by ChristianJapan

Yeah, i know. my presentation was poor. I always wanted some statistics package; now I installed R and even more clueless

Your presentation was perfectly accurate even if it wasn't splashy.

Panda's presentation, while more pleasing and colorful, is possibly misleading. The scale we select determines whether the variations between digit counts appear to be significant or insignificant. If you're devious you can even purposely choose a scale that emphasizes a bias when you want to prove a point. For example, you can use census data to prove that there's either rapid or slow growth among some particular categorization of people, just by picking scales while showing the population over time.

Here's the same data presented with a compressed scale that emphasizes the differences among the counts. OMG, the counts are so inconsistent! Technically the graph is accurate, but it shows you only part of the data, namely the very tip of the full graph. It's zoomed in too much and gives the wrong impression.

Contrast that with this graph that shows the true scale from zero. OMG, the counts are so consistent! Technically this graph is accurate but it's almost useless, and again misleading since you can't see that there are any differences among the counts.

You can solve that problem by making the graph tall enough for the differences to be visible. Click for the full-size image, then scroll to see it all. The trouble is that only mathematicians who are also basketball players or giraffes like their graphs to be that tall.

Here's another approach, showing the percentage above or below average (the difference from the "expected value") of each count. But you run into exactly the same problem because you have to choose your scale. Are these percentages large or small?

Raw data:

0	+0.16%
1	-0.06%
2	+0.15%
3	-0.18%
4	-0.06%
5	+0.17%
6	-0.01%
7	-0.05%
8	-0.04%
9	-0.08%

We have to conclude that answering LPZ's question pictorially is difficult, and no matter what graph we choose we should include the raw data as ChristianJapan did to make sure people know the facts. And of course we can also conclude that SilentPanda is up to something devious.

[SilentPanda]

Originally Posted by Doctor Q

And of course we can also conclude that SilentPanda is up to something devious.

And I would have gotten away with it too if it hadn't been for you meddling kids!

[mobilehaathi]

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.

[monokakata]

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.

[LPZ]

Originally Posted by mobilehaathi

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.

[mobilehaathi]

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)

Originally Posted by LPZ

Well, they can't end in 0, 2, 4, 5, 6 or 8. That might be reflected in your plot.

Certainly is!

[chrono1081]

I went to school in the U.S.. Math is an afterthought here.

[gnasher729]

Originally Posted by chrono1081

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

[gnasher729]

Originally Posted by mobilehaathi

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.

[ChristianJapan]

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.



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.

[mobilehaathi]

Originally Posted by gnasher729

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.

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.