103 Example

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 = 1299721 # The 100,001st prime
list_of_primes = prime_list(biggest_prime)

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

for i in range(1, 21000):
    nth_prime = list_of_primes[i - 1]
    s = str(nth_prime)

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

    digits2 = pi[:nth_prime]
    digit_sum = 0

    for digit in digits2:
        digit_sum += int(digit)

    if str(end_of).endswith(str(digit_sum)) or str(digit_sum).endswith(str(end_of)):
        print('Prime #' + str(i) + ' is ' + s)

        print(s + ' first appears in Pi at the end of ' + str(end_of) + ' digits')
        print(s + ' digits of Pi sum to ' + str(digit_sum) + '\n')

# Pi:   53, 103, 1693, 4159, 5923, 75533
# Phi:  3, 281, 203183
# e:    3547, 15401