20031205, 02:57  #1 
Jan 2003
B_{16} Posts 
Any popular way to describe the size of M40?
When I tell people about the enormous size of the numbers I'm testing I always fall short. The numbers are simply to huge, and I can't get the real size through to people. Comparing with the number of atoms in the universe doesn't do the Mersennenumbers justice since they are so much huger.
So does anyone have any good way to explain the sizes? One that really make people go "wow!" . One could try to explain how long it would take to count to M40, or rather what you could do in the same amount of time that it would take someone to count to M40 (forgetting for a while that the universe won't last that long ). Maybe something like that one guy starts counting. Real fast, say at a rate of 10 numbers each second. Then this other guy start moving grains of sand from his garden. Say at the rate of 1 grain every 100 years or 1000 years (we're in no hurry!). How much sand will he have moved from his garden before the guy is done counting to M40? (And then the answer is along the lines that he'll have moved the whole planet earth back and forth many billion times before the guy counting has come even near to a millionth of the way to M40. Or probably not even that far, I haven't done the math). I think a good and clear way of explaing the size would make for a cool footnote on the mersenne.org pages. And if people better realize the size of the enormous numbers we test, they might find the whole project more cool and exciting. So it could even help in the recrouting. What do you think? Or maybe someone allready has come up with a popular description of the numbers we test? Last fiddled with by Jorgen on 20031205 at 03:04 
20031205, 03:17  #2 
Jan 2003
11 Posts 
ok, I did some rough estimate about my sandmoving example, and I'm emberrased to say I wasn't even close in describing the real size. Maybe if the whole world was counting, dividing up the intervals. Except that one guy who is now moving one atom every millionth year. And that he'll have moved the whole universe so many times before the counting is finnished.
Or something else. Anyone? 
20031205, 03:43  #3 
Sep 2003
2^{2}×3×5×43 Posts 
In the newspaper accounts, most reporters just mention how many standard sheets of paper you'd need to use to write the number down. That's probably a concept most people could grasp.
No comparison with any physically measurable quantity is possible (grains of sand or elementary particles in the universe) because the number is just too big. If you invent some analogy that involves 10 trillion grains of sand, well if you divide M40 by 10 trillion you're left with a number that's nearly as big, and then you'd have to invent a new analogy or metaphor to explain that one. 
20031205, 04:02  #4  
Jan 2003
11 Posts 
Quote:
Quote:
Maybe you could use the odds in a lottery in some way. Say that the guy who is moving grains only does it if he winns the lottery so many times in a row. I'm looking for a way to divide the 6.5 million digit number into some prosedure or size that people are familiar with. Like, every millionth year he plays some wellknown statelottery. And if he doesn't winn first price he does nothing and waits another million years. If he winns (wich people know will be very rarely indeed) he plays it again. And again, and again. And only if he has picked the right lotterynumbers in 1 million lotteries in a row does he actually move one atom. This will get through that he's really taking his time in cleaning his garden for dirt. But still, at this extreamly slow pace, he will have moved the earth many, many times over before the counting is done. Something like that. 

20031205, 04:28  #5 
Oct 2003
Canada
47 Posts 
Several embedded analogies might not be a bad idea. Say that while the first guy is counting, the second guy would have moved so many atoms that if somebody else was to count to the number of times he'd moved the whole earth back and forth, he could move the whole earth back and forth again so many times that if somebody was to count ot that number....
The person will get the idea that there isn't really an analogy to use. You might also need to mention how many atoms there are in a grain of sand, if you aren't talking to somebody who is well aware of that. Or, Maybe speeding up the counting an order of magnitude or so? Why does the person only have to move the earth? Couldn't he move all the atoms in the solar system, several times? 
20031205, 04:46  #6  
Jan 2003
11 Posts 
Quote:
We could say that all the computers in the world, from pc's to supercomputers, are all counting nonstop. It would make the counting sound alot faster, Wich it is ofcourse, but it only buys us some 20 digits, or so. Sigh. It's hard. Quote:
Oh, well. 

20031205, 06:03  #7 
Jan 2003
Altitude>12,500 MSL
101 Posts 
It might be easier to communicate its size in terms of time. For example, writing out M40 by hand would take about a month of 'roundtheclock tireless writing at a fast pace. (quickly writing my 9digit SSN took 4 seconds)

20031205, 06:26  #8 
Sep 2003
2^{2}×3×5×43 Posts 
Of course, specifying how many sheets of paper you'd need to write the number, or how much time it would take you to write it, isn't really a measure of the prime 2^{P}1 itself. Rather, it's a measure of the exponent P.
That is, it's really a way of expressing the number 6,320,430 of decimal digits in 10^{6,320,429} ~=~ 2^{20996011}1. There just is no way to conceive of the size of the number 2^{20996011}1 itself. 
20031205, 06:37  #9 
"Gang aft agley"
Sep 2002
7252_{8} Posts 
I can't conceive the number, but I like geewiz statistics like explosions and black holes.
If it represented photons from a rubyred laser, it would be equivalent to the energy in xxx big bangs. Or if it represented hydrogen atoms, it would be enough mass for xxx black holes. 
20031205, 06:48  #10 
Jan 2003
Altitude>12,500 MSL
101 Posts 
How is writing all 6.3 million digits related to expressing exponent rather than the prime itself?

20031205, 07:13  #11  
Sep 2003
2^{2}×3×5×43 Posts 
Quote:
Precisely because a number of 6.3 million digits is roughly equal to 10^{6,299,999}... the 6.3 million is the exponent. That's like explaining the size of one billion by saying it has 10 digits, and one million by saying it has 7 digits. It sort of leaves the impression that one million is 70% of one billion. Last fiddled with by GP2 on 20031205 at 07:14 

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