 2016-03-07, 23:45 #2 VBCurtis   "Curtis" Feb 2005 Riverside, CA 2×5×463 Posts The most elementary answer: http://primes.utm.edu/howmany.html The Prime Number Theorem. Consequence 3 specifically. However, Prime95 takes into account the trial factoring effort that has been done; a candidate Mersenne that has passed TF to, say, 70 bit is much more likely to be prime than a candidate that nothing is known about. For that, you need a more complicated formula (one also presented elsewhere in this forum- I refer you to the search function, now that you have "prime number theorem" or "odds of prime" search terms). Your question 2 is answered by the first solution- if one can calculate the chances each test comes back prime, one can easily find expected number of primes in a set of 1000 or 10000 (etc) tests. If a single test has 1/50000 chance to be prime, and I run 100000 such tests, I can expect two primes. Note that is NOT the odds of finding a prime in such a range- expectation and probability are separate but related calculations.  