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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 20217 days, 23 hours, 25 minutes ago.