Thread: Odds of prime discussion View Single Post
2013-09-29, 23:14   #7
gd_barnes

May 2007
Kansas; USA

13×809 Posts

I looked at your links and I don't know enough math to verify them one way or another.

According to the odds of prime spreadsheet attached, which I created based on formulas given by one of our math experts here (ID axn), here are the chance of prime percentages that I came up with for a sieve depth of P=5T, which is how far our 3 files have been sieved:

Base / # tests / % chance

Code:
R620  3875  19.5%
R702  4896  23.7%
R916  5216  24.2%
The spreadsheet only allows entry for an average n, which is not very accurate when the nmax / nmin > ~ 1.5. So what I did was break it up into 10 mini-ranges, i.e. n=100K-110K, 110K-120K, etc., to get the expected # of primes of each and add them all up.

I'm not sure why you are showing a less chance of prime for R916 vs. R702. With bases this high, the difference in base size has little impact on % chance of finding prime. For instance, if base R702 had 5216 tests like R916 does, R702 would have a 24.9% chance of prime (vs. 24.2% for R916) so you can see there is not a lot of difference in prime chance when a base is only 30% bigger than another one if all other things are equal.

Edit: If you are using only a Nash weight to compute your chances of prime, that may explain the problem. Nash weight only works off of a sieve to P=511. Obviously a sieve to P=5T is going to be much more accurate. On our "difficulty" stats, our programming guru, Mark (rogue), uses a sieve to P=1M, which is very clearly accurate enough for determing such a stat.
Attached Files
 odds of prime.zip (5.0 KB, 174 views)

Last fiddled with by gd_barnes on 2013-09-29 at 23:24 Reason: edit