Prime generating Python code using C.P. Willans formula

Question

I wrote a prime generating code in Python, and it produces correct results. However when i want to print 8th prime I get an OverflowError:

sum += floor(pow(cos(pi * (factorial(j - 1) + 1) / j), 2))
OverflowError: int too large to convert to float

I tried to use decimal module, but I cant fix the problem.

Code:

from math import floor, cos, pi, factorial


def nth_prime(n):
    if isinstance(n, int) and n > 0:
        end_sum = 0
        for i in range(1, 2 ** n + 1):

            sum = 0
            for j in range(1, i + 1):
                sum += floor(pow(cos(pi * (factorial(j - 1) + 1) / j), 2))

            end_sum += floor(pow((n / sum), (1 / n)))

        return end_sum + 1

    else:
        raise Exception("Enter a positive integer")


print(nth_prime(8))

I tried using decimal module, but I don't know how to use it.

Answer 1

The problem occurs in this line:

floor(pow(cos(pi * (factorial(j - 1) + 1) / j)

You could use the periodicity of cos(1π) = cos(3π) etc. and analogously for the even multiples of pi. So subtract all multiples of 2π (360°) from the argument, (factorial(j - 1) + 1) / j before calculating cos.