20130917, 21:25  #1 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{3}·367 Posts 
The expected number of primes
Here's a couple of easy exercises:
1. How many primes does one expect to find in the class k*10^n1, where 2<=k<=9 and 1000000<=n<1250000. Hints for the small adjustments of probabilites:2. 10% of the range was checked and 1 prime was found. How many more primes does one expect to find?a) k is in {2,3, 5,6, 8,9} 
20130917, 21:57  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
2·3·23·31 Posts 
Shall we assume that is the first 10% by n, i.e. 1000000<=n<1025000, or something else?
Last fiddled with by MiniGeek on 20130917 at 22:30 
20130917, 22:29  #3 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
2·3·23·31 Posts 
I get:
I sieved to 100000 to get my figures. If you sieve to any other amount, you may get slightly different figures. I'm rusty at this sort of thing, but I used to do this often, so I'm fairly confident that I'm correct. Last fiddled with by MiniGeek on 20130917 at 22:31 
20130917, 23:04  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9909_{10} Posts 
Hmm, yes, roughly the lowest n values, for simplicity.
(IRL, there was a small scale survey of speeds all over the rectangle, but this was a small portion. Such a survey is helpful to be prepared for FFT length shifts, which are different for different k values.) 
20160810, 23:27  #5 
Dec 2011
After milion nines:)
2^{3}×3×5×13 Posts 
Expected number of primes is expected after all.
But in RL, on what number of primes I "must" set a goal to find at least one but for sure! I am sure that was countless combination where was expected one or two primes, but found nothing in range. So real question is: how to increase chances to find prime in range: to take more K and do less range or take less K but make wide range? 
20160811, 01:17  #6  
"Curtis"
Feb 2005
Riverside, CA
17×317 Posts 
Quote:
A list of primality tests are independent events so, whatever you do to increase the number of expected primes in your 'range', that should also increase your probability of finding a single prime. If your interests include amount of time to find a prime, you're better off with more k's rather than extending to a higher range, because larger candidates take longer to test but are less likely pertest to be prime. Last fiddled with by VBCurtis on 20160811 at 01:21 

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