Prime (#) Double Location Search

"""
# Use this code if you wish to generate Pi rather than opening it through a file
# You will need mpmath to do this
# pip install mpmath

try:
    from sympy.mpmath import mp
except ImportError:
    from mpmath import mp

print('Generating 99,999 digits of Pi...\n')

pi = ''
mp.dps = 100000
pi = str(mp.pi)[2:][:-3] + '541'        # Remove 2 characters '3.' from the front and remove 3 incorrect digits from the end
"""

pi = ''

with open('/path/to/pi.txt') as the_file: pi = the_file.read()      # This file should start without "3." in the front

#-----------------------------------------------------------------------

def prime_list(n):
    sieve = [True] * n
    for i in xrange(3, int(n ** 0.5) + 1, 2):
        if sieve[i]:
            sieve[i * i::2 * i]=[False]*((n - i * i - 1) / (2 * i) + 1)
    return [2] + [i for i in xrange(3, n, 2) if sieve[i]]

print('Generating 100,000 prime numbers...\n')

biggest_prime = 1299709 # Prime #100000
list_of_primes = prime_list(biggest_prime)

#-----------------------------------------------------------------------

for i in range(1, 100000):
    nth_prime = list_of_primes[i - 1]
    doubled = i * 2

    s = str(nth_prime)
    digits = pi.split(s)[0] + s
    end_of = len(digits)

    if doubled == end_of:
        print(str(nth_prime) + ' is prime #' + str(i))
        print(str(nth_prime) + ' first appears in Pi at the end of ' + str(end_of) + ' digits\n')

"""
Pi
71 (prime #20) first appears in Pi at the end of 40 digits
359 (prime #72) first appears in Pi at the end of 144 digits

Phi
43 (prime #14) first appears in Phi at the end of 28 digits

e
85781 (prime #8346) first appears in e at the end of 16692 digits

2Pi
5 (prime #3) first appears in 2Pi at the end of 6 digits
"""