product_of_primes_approx.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# License: GPLv3
# Date: 08 November 2016
# Website: https://github.com/trizen

# Approximation to product of primes:

#   _n_
#   | | (1 - 1/p) =~ exp(-gamma) / log(n)
#    p

# where `gamma` is the Euler-Mascheroni constant.

# See also:
#   https://trizenx.blogspot.com/2016/11/euler-mascheroni-constant.html

var p = 2
var n = 1e5

var prod = 1

while (p <= n) {
    prod *= (1 - 1/p)
    p.next_prime!
}

var approx = exp(-Num.EulerGamma)/log(n)
say "#{prod.round(-10)} =~ #{approx.round(-10)}"