20100421, 17:29  #1 
1091_{10} Posts 
GIMPS: much worse odds than the lottery?
The odds of getting 5 out of 5 on the Mega millions lottery is 1 in 56*55*54*53*52/(5*4*3*2*1) = 1 in 3,819,816. The prize is $250,000, and a lot more if you can somehow get the mega number right. As most of you know, one dollar buys one ticket.
The odds that a 100 million digit mersenne candidate factored to 76 bits will be prime is 1 in 2,556,600 (using the formula (how_far_factored1) / (exponent times Euler's constant). A good computer will take a year and a half to test one 100,000,000 digit number, and the prize is $150,000. A year and a half is 13,140 hours, and most computers use ~50 watts more when they're busy compared to when they're idle. That comes out to 657 kilowatthours, so it'll cost you $72 to test one number, assuming you're charged at the U.S. average of 11 cents per kilowatt hour. So if you spend $72 on GIMPS, your odds of winning $150,000 are 1 in 2,556,600. But if you were to spend that same amount of money on the lottery, your chances of winning $250,000 or more are 53,053. Do these numbers look right? 
20100421, 19:15  #2 
"Jacob"
Sep 2006
Brussels, Belgium
11×173 Posts 
Your numbers minimise the cost of running GIMPS, you have to buy the computer, electricity costs are much higher in some places of the world...
If you are in it to make money, you have a better thing to do : just save your money and do not participate in GIMPS and do not play the lottery. (The lottery is a bad investment as well : to be sure to earn 250 000 USD you have to spend 3 819 816 USD.) Gimps is not about the EFF prise, it can add to the excitement, but it is about something else. Jacob Last fiddled with by S485122 on 20100421 at 19:19 
20100421, 19:34  #3 
6809 > 6502
"""""""""""""""""""
Aug 2003
101ร103 Posts
2^{2}·7·389 Posts 

20100421, 19:47  #4 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×3×29×67 Posts 

20100421, 19:48  #5 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×3×29×67 Posts 

20100421, 19:58  #6 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11×389 Posts 
http://www.mersenne.org/legal/#awards
If you use Prime95/mprime and/or participate in GIMPS, you have to adhere to the above rules. You'd only get $50,000 of it. Also, from those rules, if you find a prime below 100M digits, GIMPS will award you $3,000 (may change from $1,000 to $5,000). Feel free to use that to try to find the odds of making up for the electricity by finding a smaller prime. The lottery, on average, doesn't return anything like what is put into it. The 10M digit prime award was an even worse average return. The 100M digit prime award is even worse than the 10M digit award, as you've discovered. Besides that, there are some inaccuracies, such as ignoring the cost of a computer, the total power cost (instead of just the "extra" cost of running Prime95 vs idle), AC costs, etc. (all of which play a more and more serious role if you decide to buy multiple computers for this task) Last fiddled with by TimSorbet on 20100421 at 20:07 
20100421, 20:28  #7  
Oct 2008
n00bville
2^{5}·23 Posts 
Quote:
Beside having this discussion again ;) ... to marry is IMHO a far worse investment and I gladly invest a minimum amount in the lottery instead of drinking and smoking or having a female financial black hole (=wife) at home (like many of my colleges). By the way my prime95 shows a chance of 1 to 250.000 for finding a 100m prime (with one worker thread). Last fiddled with by joblack on 20100421 at 20:31 

20100421, 22:28  #8  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
joblack and his friends may be in that group. I used to be married to someone in that group. After all, once you've seen a movie for which you bought a ticket, you don't have the money you spent, but you have memories of the movie. Some folks really, really like getting a thrill, such as rollercoaster fans. Once they've had their rollercoaster ride, what do they have for their money? Lower odds than any lottery at those two events (though I did get a refund once when a theater movie projector failed). ... and also there are just plain gamblers. All of the above may be quite knowledgeable about the math. 

20100421, 22:52  #9  
Oct 2008
n00bville
2^{5}×23 Posts 
Quote:
I suspect that more than half of the prime hunters aren't doing it just for 'scientific advances' but for the thrill to personally find a prime number (and to be immortal as a Mersenne prime number discoverer). At least that's part of my motivation ... Last fiddled with by joblack on 20100421 at 22:56 

20100425, 09:43  #10 
Nov 2008
San Luis Obispo CA
2^{7} Posts 

20100425, 10:24  #11 
Jul 2006
Calgary
110101001_{2} Posts 

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