google_prime_id.py

def factiorials(max_n):
    f = [0]
    x = 1
    for i in range(1, max_n+1):
        x *= i
        f.append(x)
    return f
def isPrime(j, f):
    return (f[j-1]+1)%j == 0
def solution(n):
    max_int= int((n+5)*(5000/2465)+475)
    facts = factiorials(max_int)
    id_str = ''.join([str(x) for x in range(2, max_int+1) if isPrime(x, facts)])
    return id_str[n:n+5]

from time import perf_counter
start = perf_counter()
for i in range(10000):
    s = perf_counter()
    print(i, solution(i), f"completed in: {perf_counter()-s}s")
print(f"elapsed {perf_counter()-start}")