Euler product formula and Riemann zeta function

     The product in the Euler product formula is taken over all the prime numbers p. This product equals the zeta function ζ(s). The sum of the terms of ζ(s) converges for s > 1.
If you input real s > 1 and the number of factors k in the product formula (k corresponds to the kth prime number) the program calculates ζ(s) and the product of k factors of the Euler product formula.
ζ(s) equals the product of all (infinitely many) factors. If you take k higher the result of the product comes nearer to ζ(s). It is not necessary to enter the primes themselves. The program generates them. The calculation of ζ(s) is an approach of its limit (straight summation of 1000000 terms). The Euler product of k factors is another approach of this limit. You can compare both approximations.

s ∈ R, s > 1 :      k ∈ N+ :