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/** This program calculates primorial numbers. A primorial is the product
of primes.
primorial[0] = 1 (by definition)
primorial[1] = 2
primorial[2] = 6
primorial[3] = 30
This does not do any caching of results.
*/
primorial[n] := product[first[primes[], n]]
/** This is a recursive algorithm that splits the results into an upper and
lower half and multiplies in stages. This is much faster for large
numbers. */
primorialSplitting[n] :=
{
if n == 0
return 1
primes = array[first[primes[], n]]
return primorialSplitting[n, 0, n-1, primes]
}
/** The actual recursive algorithm. */
primorialSplitting[n, begin, end, primes] :=
{
range = (end-begin)
if range >= 2
{
middle = (begin + end) div 2
return primorialSplitting[n, begin, middle, primes] * primorialSplitting[n, middle+1, end, primes]
}
if range == 1
return primes@begin * primes@end
if range == 0
return primes@begin
}
/** Rosetta code tests.
https://rosettacode.org/wiki/Primorial_numbers
*/
for n = 0 to 9
println["primorial[$n] = " + primorialSplitting[n]]
for n = [10, 100, 1000, 10000, 100000, million]
println["Length of primorial $n is " + length[toString[primorialSplitting[n]]] + " decimal digits."]
Download or view primorial.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 19966 days, 7 hours, 30 minutes ago.