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Message boards : Number crunching : Top Prime Finders

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John
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Message 8728 - Posted: 14 Apr 2008 | 22:13:08 UTC

We have released an updated Top Prime Finders page, which now counts primes found in all subprojects. The prime numbers are assigned a score which differs according to prime number size, so a giant Woodall prime is "worth" more than a smaller TPS prime."

Top Prime Finders - also located in the left menu

Legend
Primary check = primes found
Double Check = primes double checked
Total = Primary check + Double check
Score = number equivalent to 100,000 digit prime (i.e. a score of 19 represents 19 100000 digit primes)
BOINC Credit = BOINC credit

Scoring Information
The scoring formula is similar to the one used at The Largest Known Primes Database. However, PrimeGrid awards 1/2 points to double checkers. Also, we only display the "normalized" score based on a 100,000 digit prime instead of the 5000th prime which is ever changing.

An indiviudal's total score is the sum of all their primary finds and double checks. Double checks receive 1/2 the score of the primary.

Generally speaking, the score is based on the "difficulty" of finding the prime. Clearly a 1,000,000 digit prime is much harder to find than a 100,000 digit prime. Based on our minor changes, here's the formula for score:

Given: k*b^n+/-1
log_n = ln(k) + n*ln(b)

score = (log_n)^3 * ln(log_n) / 100,000 digit score

For example, using 7668057255*2^666667-1, leaving out the 100,000 digit score section for now, we get the following:

log_n = ln(k) + n*ln(b)
log_n = ln(7668057255) + 666667*ln(2)
log_n = 22.7603 + 462098.3514
log_n = 462121.1117
score = (log_n)^3 * ln(log_n)
score = (462121.1117)^3 * ln(462121.1117)
score = 9.86887E+16 * 13.0435
score = 1.28725E+18

As mentioned earlier, we "normalize" this to a 100,000 digit prime. Applying that, we get the following:

score of a 100,000 digit prime is 1.50733E+17

score = prime score / 100,000 digit score

score = 1.28725E+18 / 1.50733E+17
score = 8.5400

Therefore, the prime 7668057255*2^666667-1 is equivalent to finding 8.54 100,000 digit primes. The primary finder would be awared 8.54 points and the double checker would be awarded 4.27 points since the double checker gets 1/2 credit.

A typical TPS score at n=333,333 is approximately 1.01 points with double check getting 0.51 points.
____________

[B^S] Astral Walker

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Message 8729 - Posted: 15 Apr 2008 | 0:13:05 UTC - in response to Message 8728.

Score = number equivalent to 100,000 digit prime (i.e. a score of 19 represents 19 100000 digit primes)

Given: k*b^n+/-1
log_n = ln(k) + n*ln(b)

score = (log_n)^3 * ln(log_n) / 100,000 digit score

Just out of curiousity, if the scores are based on the number of decimal digits, why are you using natural logarithms?

John M. Johnson "Novex"
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Message 8731 - Posted: 15 Apr 2008 | 3:09:36 UTC

Thanks so much John for implementing this great new option :)

As always you have my respect.
____________

John M. Johnson "Novex"

BobW

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Message 8734 - Posted: 15 Apr 2008 | 11:02:03 UTC

Just a question - Are there some prime finds that are being disallowed or otherwise skipped on this page? For example, I show up with 23 primes found and 12 doublechecked, for a total of 35, but my account page and the certificate of computation show 45 TPS primes found (and so did the old version of the page).

Is it just that the new page is somehow behind the times in what it is counting or is it related to a problem in reporting - since I haven't gotten any notices to report any of the new primes since February?
____________

pan2000
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Message 8738 - Posted: 15 Apr 2008 | 13:51:24 UTC - in response to Message 8734.

Same problem here. Missing 19 primes.

Rytis
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Message 8739 - Posted: 15 Apr 2008 | 15:33:02 UTC

I believe that the new database is showing correct numbers. The issue with inflated counts in your account page is the same as it was with factors being counted more than once when validator was having issues. The current table has all primes that you found, and the stats page simply counts them.

In any case, I will look into it. I've squeezed it into my schedule for Thursday evening.
____________

John
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Message 8749 - Posted: 15 Apr 2008 | 23:31:44 UTC - in response to Message 8729.

Score = number equivalent to 100,000 digit prime (i.e. a score of 19 represents 19 100000 digit primes)

Given: k*b^n+/-1
log_n = ln(k) + n*ln(b)

score = (log_n)^3 * ln(log_n) / 100,000 digit score

Just out of curiousity, if the scores are based on the number of decimal digits, why are you using natural logarithms?

Just note that we are "borrowing" this formula from The Largest Known Primes Database. However, to answer your question,
it is my understanding that natural log is a more commonly used expression in mathematics. Wikipedia has a nice explanation as to why this may be the case:
Initially, it might seem that since our numbering system is base 10, this base would be more “natural” than base e. But mathematically, the number 10 is not particularly significant. Its use culturally—as the basis for many societies’ numbering systems—likely arises from humans’ typical number of fingers.[2] And other cultures have based their counting systems on such choices as 5, 20, and 60.[3][4][5]

Log e is a “natural” log because it automatically springs from, and appears so often, in mathematics.

If you wish, you can use log base 10 instead of log base e (ln) in the expression. It will produce similar results.

Thanks so much John for implementing this great new option :)

As always you have my respect.

Thanks! However, I'll have to transfer this to Rytis as he is the one who did all the technical work. :)
____________

John M. Johnson "Novex"
Volunteer tester

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Message 8750 - Posted: 16 Apr 2008 | 8:45:56 UTC - in response to Message 8749.

Thanks so much John for implementing this great new option :)

As always you have my respect.

Thanks! However, I'll have to transfer this to Rytis as he is the one who did all the technical work. :)[/quote]

Ah I actually have been leaving him to his semester finals which I know first hand can be sometimes crazy. But I really do appreciate the effort in which this great community helps one another. I humbly respect you great mods and this wonderful community :)

____________

John M. Johnson "Novex"

[B^S] Astral Walker

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Message 8755 - Posted: 16 Apr 2008 | 15:25:36 UTC - in response to Message 8749.

Just note that we are "borrowing" this formula from The Largest Known Primes Database. However, to answer your question,
it is my understanding that natural log is a more commonly used expression in mathematics. Wikipedia has a nice explanation as to why this may be the case:

Thanks for the reply. I know it really makes no difference what base logarithm you use for determining the score. It was just idle curiousity as all mentions are of decimal digits. :)

Rytis
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Message 8764 - Posted: 18 Apr 2008 | 17:41:10 UTC - in response to Message 8739.

I believe that the new database is showing correct numbers. The issue with inflated counts in your account page is the same as it was with factors being counted more than once when validator was having issues. The current table has all primes that you found, and the stats page simply counts them.

In any case, I will look into it. I've squeezed it into my schedule for Thursday evening.

Thanks to BobW, I think I found some missing primes. Do you think it's OK now?
____________

John M. Johnson "Novex"
Volunteer tester

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Message 8765 - Posted: 18 Apr 2008 | 18:18:04 UTC

Unfortunately mines still not showing any of the double checks.
____________

John M. Johnson "Novex"

Rytis
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Message 8766 - Posted: 18 Apr 2008 | 18:38:58 UTC - in response to Message 8765.

Unfortunately mines still not showing any of the double checks.

Because the initial finder still has not reported them to the prime pages.
____________

John M. Johnson "Novex"
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Message 8767 - Posted: 18 Apr 2008 | 23:22:17 UTC

Ah, that would explain it then. Thanks a ton Rytis, as always you have my respect.
____________

John M. Johnson "Novex"

[B^S]ST47

Joined: 12 Jul 05
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Message 8898 - Posted: 29 Apr 2008 | 10:35:48 UTC

My 'your account' page says I have one tps prime, but I cannot find myself on the list, and I don't see any way to find the work unit it's talking about

____________

[B^S] Astral Walker

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Message 8899 - Posted: 29 Apr 2008 | 14:18:12 UTC

It's the one with 2.90 credits instead of 1.45.

28582520

I'm not sure why you get the strange message but this is a prime number.

Warning: mysql_fetch_object(): supplied argument is not a valid MySQL result resource in /home/boinc/proj/html/project/project.inc on line 274
*2^-1 is not prime.

[B^S]ST47

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Message 8909 - Posted: 29 Apr 2008 | 23:32:17 UTC

I looked, it must have only recently been validated. I'm still not on the page http://www.primegrid.com/primes/?section=topusers&by=score though?
____________

John
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Message 8910 - Posted: 30 Apr 2008 | 0:04:25 UTC - in response to Message 8909.

I looked, it must have only recently been validated. I'm still not on the page http://www.primegrid.com/primes/?section=topusers&by=score though?

You were the double checker...and the primary checker has not reported it to the Prime Pages yet. It will show up after they report it.
____________

[B^S]ST47

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Message 8916 - Posted: 30 Apr 2008 | 10:38:13 UTC

Ah, OK. This system is very confusing. I like the old days of BOINC when they didn't let us users get into the technical stuff :)
____________

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Message 11188 - Posted: 18 Oct 2008 | 7:17:10 UTC

Are found primes reported automatically to The Largest Known Primes-List and if so when/how often? Or do i/we have to report them ourselves?
I am somewhat puzzled here... ;)

pschoefer
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Message 11189 - Posted: 18 Oct 2008 | 10:30:54 UTC - in response to Message 11188.

Are found primes reported automatically to The Largest Known Primes-List and if so when/how often? Or do i/we have to report them ourselves?
I am somewhat puzzled here... ;)

They are reported automatically, if you give the permission in your preferences. Else you should get an email with the reporting instructions.

At the moment, only primes found in Cullen, Woodall, 321 and PSP LLR subprojects are big enough for the list, TPS and PPS LLR are too small (we have to reach n~350k for big enough numbers ;)).
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Message 11194 - Posted: 18 Oct 2008 | 12:23:29 UTC

A-OK! Thanks for clarification.

Message boards : Number crunching : Top Prime Finders