Talk:Primorial numbers

PARI/GP you speak about factor tree, but only primes are used, where is the advantage??? I love such solutions like in perl <lang perl>use ntheory qw(pn_primorial); say "First ten primorials: ", join ", ", map { pn_primorial($_) } 0..9;</lang> and all is done ;-) Horsth

a faster-than-exponential growth rate in CPU time stated by dinosaur

school - multiplication ist quadratic in runtime O(count of digits) ~ (count of digits)^2

Prime(100000) = 1299709, Primorial(100000) ~ 0.1909604E+563921                      121.547 seconds.
Prime(1000000) = 15485863, Primorial(1000000) ~ 0.1147175E+6722809                17756.797 seconds.

10-times Numbers -> ~100-times runtime 121*100-> 12100

the digitcount of the numbers one multiplies grew be a factor of lg10(15.45Mio)/lg10(1.299Mio) =1,17

so you get 10-> (1.17*10) ^ 2 = 136,89*121,547= 16638 thats not far from 17756

Now take into account that the number gets so big, that it doesn't fit in level3 Cache ,which slow things down.Only 3% will be enough 121,547*(1.17*1.03*10)^2 s = 17651 s Horsth

The implementation of primorial I am using, running on this laptop, took 0.002909 seconds for primorial 100000 and 0.049093 seconds for primorial 1000000. With digit counts, that became 0.004267 seconds and 0.04369 seconds. I guess that's faster than exponential growth rate if by fast you mean the execution time... but ... actually, I'm not sure where I'm going with this. I am mildly surprised that digit count could be faster than the raw primorial but that might just be random variation --Rdm (talk) 20:41, 8 April 2016 (UTC)