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_factored-1) / (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 kilowatt-hours, 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?

[S485122]

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

[Uncwilly]

Originally Posted by S485122

(The lottery is a bad investment as well

That is blatantly false. It is not a bad investment. It is a voluntary tax on those that are bad at math.

[xilman]

Originally Posted by Uncwilly

That is blatantly false. It is not a bad investment. It is a voluntary tax on those that are bad at math.

A beautiful characteristic of the UK lottery is that it is a popular voluntary tax on the statistically challenged.

Paul

[xilman]

Originally Posted by Uncwilly

That is blatantly false. It is not a bad investment. It is a voluntary tax on those that are bad at math.

As I observed earlier, many in North America don't do irony.


Paul

[TimSorbet]

Originally Posted by Unregistered

... and the prize is $150,000.

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)

[joblack]

Originally Posted by xilman

A beautiful characteristic of the UK lottery is that it is a popular voluntary tax on the statistically challenged.

Paul

Not right. I know the odds (so does a lot of my friends) and we still play lottery (Euro Millions).

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).

[cheesehead]

Originally Posted by Uncwilly

That is blatantly false. It is not a bad investment. It is a voluntary tax on those that are bad at math.

There is another set of lottery fans who understand the odds, but do it for entertainment, for the thrill of imagining what it would be like to win, or something like that.

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 roller-coaster fans. Once they've had their roller-coaster 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.

[joblack]

Originally Posted by cheesehead

There is another set of lottery fans who understand the odds, but do it for entertainment, for the thrill of imagining what it would be like to win, or something like that.

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 roller-coaster fans. Once they've had their roller-coaster 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.

You're right - I'm a gambler - but in a calculated way. I don't play extensive lottery but for the minimal chance to win. I also used to play Hold'em Poker.

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 ...

[Freightyard]

Originally Posted by Unregistered

That comes out to 657 kilowatt-hours...to test one number

Does GIMPS cause global warming? Perhaps it should be banned. I'm calling Al Gore.

[lfm]

Originally Posted by Freightyard

Does GIMPS cause global warming? Perhaps it should be banned. I'm calling Al Gore.

We are very efficiently using the energy to find mersenne numbers. No other mersenne search has ever been as efficient.