How to Tell if my Number Qualifies for the Prize
 

I guess subject says it all. Do I have to reserve them manually, or will I be given one to work on that is big enough. Sorry if this is an obvious question, I'm new to the GiMPS thing and didn't see it anywhere.

Thanks

WS

All you have to do is select the following work type in Prime95:

[B][FONT="Courier New"]100,000,000 digit numbers to test[/FONT][/B]

under Test -> Worker Windows -> Type of work to get
You will be assigned a number 332192831 or larger (which is the first number that can qualify for the next prize).

[QUOTE=Uncwilly;254589]All you have to do is select the following work type in Prime95:

[B][FONT=Courier New]100,000,000 digit numbers to test[/FONT][/B]

under Test -> Worker Windows -> Type of work to get
You will be assigned a number 332192831 or larger (which is the first number that can qualify for the next prize).[/QUOTE]

... which is how to have a chance of winning the real jackpot of $50000 for the first to discover a prime number with at least 100M decimal digits.

Do note though that these tests typically take a couple of years or more to complete with current technology. And it's still possible, if I'm not mistaken, to win a more modest prize for discovering any new Mersenne Prime. Simply choose the LL-first time test work type to have a chance at this (not LL double checks which are extremely unlikely to discover a prime because that could only happen if the first-time test was incorrect). If you are specifically hoping to discover the largest known Mersenne Prime, choose the option LL test for world record: this allocates you a number which is higher than the currently known largest Mersenne Prime, though of course someone else could discover an even higher one while you are testing.

See [URL]http://v5www.mersenne.org/legal/default.php#awards[/URL] for details of the prizes.

To summarise:

To have a chance of winning $50,000, choose a 100 million digit test.

To have the best chance of winning $3,000, choose the smallest available first-time test. World-record tests (and doublechecks) also qualify for the $3,000 prize, but you may be slightly (will be much) less likely to be successful.

The other assignment types - Trial Factoring, P-1 and ECM - contribute to GIMPS progress, but they do not qualify for prizes.

[QUOTE=Mr. P-1;254651]To have a chance of winning $50,000, choose a 100 million digit test.

To have the best chance of winning $3,000, choose the smallest available first-time test. World-record tests (and doublechecks) also qualify for the $3,000 prize, but you may be slightly (will be much) less likely to be successful.[/QUOTE]

Let's quantify those. (Please replace my numbers with more reasonable ones if known; I'm working off the top of my head.) It may take 5 times as long to do a 100M digit test as a first-time test, and coupled with the larger size your chances of finding one of those are something like 19% that of finding a prime on the first-time check. It may be 4 times faster to do a double-check than a first check, and the numbers are smaller and thus would be more likely to yield a prime, but they've already been checked with an error rate of, say, 3%. This makes your chances something like 12.5% that of finding a prime on a first-time check.

[QUOTE=CRGreathouse;254660]Let's quantify those. (Please replace my numbers with more reasonable ones if known; I'm working off the top of my head.) It may take 5 times as long to do a 100M digit test as a first-time test,[/QUOTE]
IIRC a 100M digit test takes ~4.1 core years. A current LL takes closer to 1 core month. So it is ~50:1.

[QUOTE=Uncwilly;254667]IIRC a 100M digit test takes ~4.1 core years. A current LL takes closer to 1 core month. So it is ~50:1.[/QUOTE]

Wow, that much of a difference? I just figured time was essentially quadratic and doubling length quadrupled time. Is the ratio with the double-check primes that great? (I'm not sure where the doublecheck wavefront is right now.)

Also needs checking: the error rate.

[QUOTE=CRGreathouse;254668]Wow, that much of a difference? I just figured time was essentially quadratic and doubling length quadrupled time. Is the ratio with the double-check primes that great? (I'm not sure where the doublecheck wavefront is right now.)[/QUOTE]The current wave front for first time ~50,000,000. 100M digit ~332,000,000.

[QUOTE=Uncwilly;254670]The current wave front for first time ~50,000,000. 100M digit ~332,000,000.[/QUOTE]

And for double-checks?

[QUOTE=CRGreathouse;254672]And for double-checks?[/QUOTE]
Using James H's tool here: [url]http://mersenne-aries.sili.net/credit.php[/url]

_27,000,000 = ___26.8 GHz/days of credit (current area for DC's)
_50,000,000 = __105.0 GHz/days of credit (current area for first time)
332,192,831 = 5,730.3 GHz/days of credit (first 100M digit number)

Divide by your cores and/or clock speed to get an idea of how long it will take to do a test.

[QUOTE=Uncwilly;254674]Using James H's tool here: [url]http://mersenne-aries.sili.net/credit.php[/url]

_27,000,000 = ___26.8 GHz/days of credit (current area for DC's)
_50,000,000 = __105.0 GHz/days of credit (current area for first time)
332,192,831 = 5,730.3 GHz/days of credit (first 100M digit number)

Divide by your cores and/or clock speed to get an idea of how long it will take to do a test.[/QUOTE]

Great! So if the error rate is E (say, E = 0.03) you get about 4.06E (say, 0.122) expected discoveries with double-check and 0.0166 with 100M.

Not that maximizing expected prizewinnings is a sensible strategy, but if that were the goal first checks are 4 times better than 100M which are twice as good as double checks. (For the worst of all worlds, try double-checking 100M candidates.)