[QUOTE=R.D. Silverman]
The person who finds it will, almost certainly, have made no contribution
to computer science, to mathematics, or to our general knowledge
other than mindlessly donating computer time (that he/she doesn't need)
to run software that was the brilliant work of someone ELSE. [kudos to
George!!!! :banana: :bow: ][/QUOTE]

Then again, those people who "mindlessly" contribute computer time were the original motivation for a highly skilled person like George to write Prime95 in the first place. And every once in a while, one of the "cpu time borgs" might be interested enough in how GIMPS works anyway that they start to read up on the subject. At least that's what happened in my case. I probably won't make a significant contribution to number theory, but I have contributed some code to factoring algorithms and hope to continue to do so. And I'm hardly the only one who developed an earnest interest in the subject thanks to GIMPS.

I'd write more, but I'm too drunk right now - I celebrated successful exams together with another CS guy I know, who's called (of all names) "Hans Hacker". :smile:

Alex

[QUOTE=alpertron]This is an interesting approach. The only problem I see is that M_p has only 2098960 digits. Maybe it would be better to start with the biggest known Mersenne prime and then multiply other "small" numbers (maybe taken from Caldwell database) in order to be near ten million digits.[/QUOTE]

Perhaps he meant M_p for p=13466917, with slightly over 4 million digits. One could use p=25964951, but the extra padding of 6 million digits as opposed to 2.2 million digits should help in eliminating more small factors, thereby increasing the density of primes in his sequence.

I played around with the form n*(M_p)^2+1 for awhile, as there is a nice test for primality, but p=20966011 already puts one over 12.6 million digits, increasing the cost of tests.

[QUOTE=philmoore]Perhaps he meant M_p for p=13466917, with slightly over 4 million digits. One could use p=25964951, but the extra padding of 6 million digits as opposed to 2.2 million digits should help in eliminating more small factors, thereby increasing the density of primes in his sequence.

I played around with the form n*(M_p)^2+1 for awhile, as there is a nice test for primality, but p=20966011 already puts one over 12.6 million digits, increasing the cost of tests.[/QUOTE]


Yes. I cut and pasted the wrong exponent.

[QUOTE]Humpty Dumpty[/QUOTE]
Oh no, GIMPS has you on the payroll now?



[QUOTE]But its goals, with probability 1, necessitate it hunting for >=10M-digit primes.[/QUOTE]
And other non-10M, which make up a large portion of the 3%.
You are misrepresenting a little, although your point as devil's advocate is well taken. Sob is the only other indirect competition, that has a great production score to date.



[QUOTE]Will RMA.NET run on my G5 Mac or my DEC Alpha?[/QUOTE]
Who in the mainstream (US bulk) runs these? In the future?
Would they run anywhere near as fast? Not familiar actual question.
Again you are misrepresenting a bit.



[QUOTE]Will it? By when?[/QUOTE]
Yup, and it would have to be soon, though there are multiple prizes to aim for.
Perhaps Operation Billion digits, is not such a bad idea, depending on the future hardware improvements.



[QUOTE]Woh - curveball! I also hear the price of tea in china is going through a short term boost due to increased demand in eastern Europe, and reduced supply due to inclement weather in the region.[/QUOTE]
Now this is clearly a dig, please do not trivialize my knowledge in this field.
I am more credible than you, in this case.

[QUOTE=R.D. Silverman]It is worse than a PITA.

Eventually, someone will find a 10M digit prime. Big Whoopee.

The person who finds it will, almost certainly, have made no contribution
to computer science, to mathematics, or to our general knowledge
other than mindlessly donating computer time (that he/she doesn't need)
to run software that was the brilliant work of someone ELSE. [kudos to
George!!!! :banana: :bow: ]

Yet, the person who succeeds will get a fat check. (Maybe he should get
a fat chick instead????) [do any women participate in this search, or is
it strictly a guy thing?]

Why not just hold a lottery and be done with it???

I might have some respect for the prize if it was required that the one
finding the prime WROTE HIS/HER OWN CODE, and had to submit said
code along with the prize.[/QUOTE]

I mostly concur. The final paragraph, depending on interpretation, unfortunately limits the number of searchers to nigh-on-nobody. 50 people in the world, perhaps. I'm not entirely sure I'd fit into that category, with the strictest interpretation, as I use variously DJB's and YG's FFT libraries under my own novel DWTs. There's no way I could write a fast FFT library from scratch. (Although I think I'm making progress making DJBFFT faster, but it's still undeniably DJB's code.)

Certainly, almost the entirity of the award goes to the brains, not the brawn. And that's George in GIMPS's case. And in SoB's case. And in RieselSieve's case. ...

It's not entirely a guy thing. I bounce mathematical ideas off my girlfriend frequently (although that might be a case of "if you explain it to someone else you get to understand it better yourself"), and from a creative and administrative level she contributes enormously to my projects.

[QUOTE=fatphil](although that might be a case of "if you explain it to someone else you get to understand it better yourself")[/QUOTE]

I know that feeling very well. I try to explain things which I often don't understand myself. But it improves ones own understanding of the problem!

Maximizing winning chances
 

Hello,
I don't really understand the difference between LL test and the 10 000 000 digit test. What should I choose to maximize my winning chances? The LL test gives 5000$ if you find a prime, and the other gives 50 000$, but you have less chance of finding? Is that correct?

Maybe you should make a 'how to maximize your winnings' page for the people that are just in it for the money. It's the same for you, as you are in it for the mathematical challenge

Well, the probabilities are changing continually as participants reserve and complete testing of exponents. However, I can say for sure that your chances of finding any prime are smaller if you search 10,000,000+ digit numbers than 10,000,000- digit numbers because 1) Each test takes more time, so you will have time for less tests and 2) Each candidate has a smaller chance of actually being prime.

So, if I just want to win some money, the best chance is just letting the program run.

But is it correct that if I find a prime with the LL method, I get 5000$?

[QUOTE=Unregistered]So, if I just want to win some money, the best chance is just letting the program run.

But is it correct that if I find a prime with the LL method, I get 5000$?[/QUOTE]

Actually, I can construct a strategy for you that will increase your expected
return. But I would need to have some information about your utility
expectation function (e.g. would you rather have a 10% chance of $100K
or a 50% chance at $20K, or a 100% chance at 5K etc.) What if it is a
10% chance at $1M versus a 100% chance at $10K??

Also, since you are doing this for money, I would need to charge for my
professional services. My fees are $200/hr, with a 2 hour minimum.

[QUOTE=Unregistered]So, if I just want to win some money, the best chance is just letting the program run.

But is it correct that if I find a prime with the LL method, I get 5000$?[/QUOTE]

You should test 10 million digit numbers. There is no guarantee that a smaller prime will get you $5000. Read the prize rules carefully.