Uses a hybrid table lookup and sieving algorithm. Also provides the option of using PARI's sieving algorithm, Andrew Ohana's optimized Legendre algorithm, or Victor Miller's Lagarias Miller Odlyzko (LMO) combinatorial algorithm.
Be sure to use the -m32 option when compiling the c code, and if necessary, download the required libraries to run 32 bit code on your computer. Macbook pros should be the easiest to work. The table of values of the prime counting function comes from http://www.primefan.ru/stuff/primes/table.html The gap between values in the table is the same for each decade, and then jumps to a larger value. The performance of my prime_pi(x) is best near values of x in the table, and worst for values halfway between. The performance decreases after each power of 10, where the gap between table entries increases. I would like my code to be run against Mathematica on the same machine. It would be appropriate to create a random set of values in each decade (i.e. values all with some number of digits) for prime_pi. For nth_prime, this would work, but for a better picture of the performance of my code, it would be appropriate to make a random set of values of n (to give to the nth_prime function) such that nth_prime is between two successive powers of 10 (i.e. nth_prime is some number of digits long) for each number of digits. See http://en.wikipedia.org/wiki/Prime-counting_function#Table_of_.CF.80.28x.29.2C_x_.2F_ln_x.2C_and_li.28x.29 for a table of prime_pi. Kevin Stueve --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
