mersenneforum.org Amusing stats: luckiness of NPLB members
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2010-06-04, 22:19   #1
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

10AB16 Posts
Amusing stats: luckiness of NPLB members

I was wondering if I was luckier than most people in how many primes I find for my work.
How do I define "lucky"? With statistics, of course. I compare the ratio of prime scores to pair scores. So if you get more primes than you "should", that number will be higher, and if you get less, it will be lower. I've attached the results. (I know something trying to calculate the chances of primes would be more accurate than comparing against other people, but that would be much harder and only a little more accurate.)
I calculated the scores signifying luckiness as Prime Score / Pair Score * 100000. (using data from the NPLB database as of the 2010-06-04 16:09:46 update)
I included both a CSV with all users, and one only including users that have searched at least 5000 pairs, to eliminate most 0 scores and any anamolous results (e.g. Razor_FX_II's 57 score). I also included the full ODS file, which displays the scores to a higher precision and has a graph and stuff.
Of the ones with at least 5000 pairs searched, (51 people) here are the min, Q1, median, Q3, and max scores: 0.0000, 14.4503, 18.5166, 21.4824, 36.3916.

I'm at the 76th percentile. So yes, I am luckier than the average prime searcher.
More trivia: gd_barnes and kar_bon are quite average, at 46th and 50th percentile, respectively. mdettweiler is unlucky, at the 20th percentile.
Attached Files
 NPLB lucky stats.zip (38.1 KB, 94 views)

Last fiddled with by Mini-Geek on 2010-06-04 at 22:30

2010-06-04, 23:55   #2
mdettweiler
A Sunny Moo

Aug 2007
USA (GMT-5)

186116 Posts

Quote:
 Originally Posted by Mini-Geek More trivia: gd_barnes and kar_bon are quite average, at 46th and 50th percentile, respectively. mdettweiler is unlucky, at the 20th percentile.

 2010-06-05, 01:35 #3 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 912810 Posts “The more I practice, the luckier I get.” /Gary Player/ Last fiddled with by gd_barnes on 2010-06-05 at 20:47 Reason: request from Batalov to edit
 2010-06-05, 09:14 #4 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 10110011001012 Posts I am 42nd percentile. I am in a huge prime gap for all projects(top 5000). I have done lots of searching at both NPLB and CRUS in the top 5000 range and have found nothing. Thats excluding the work I did on my own in the rieselprimedatabase subforum which I have failed to find any top 5000 primes for since this started.
 2010-06-05, 20:48 #5 gd_barnes     May 2007 Kansas; USA 27F316 Posts I got an Email request from Batalov to edit his post in this thread. That has now been done.
 2010-06-05, 21:05 #6 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 23·7·163 Posts Yes, thanks, -- I was looking for a thought and found a totally wrong way of expressing it, initially. Gary Player has got it right.
2010-06-11, 13:12   #7
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17×251 Posts

With this prime:
Quote:
 Originally Posted by Mini-Geek 349*2^1228715-1 is prime!
I jumped to around (I only recalculated my score, not everyone's) the 90th percentile. My prime score/pair score * 100000 is now 30.4852262924, which is 1.45 standard deviations above the mean.
This move actually brings the list as a whole closer to what should be expected if the primes are normally distributed between everybody.

If the data are normally distributed, we expect about b% of the values to lie within a standard deviations of the mean. It is now c%, before this change it was d%.
Code:
a     b%      c%      d%
1 68.27%  68.63%  70.59%
2 95.45%  92.16%  90.20%
3 99.73% 100.00% 100.00%
If I had found no primes so far in my individual k work, I would be below the average, with a score of 13.0456164305. 18th percentile, a little lower than mdettweiler. 5.13 points, or 0.63 std devs, down from the mean.
If I had found 1 prime so far in my individual k work, I would be just above the average, with a score of 20.4967036288. 72nd percentile, but only 2.17 points, or 0.27 std devs, up from the mean.
Those big primes make a big difference, even with someone like me who has a significant amount of work behind it.

Last fiddled with by Mini-Geek on 2010-06-11 at 13:23

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