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Part 1

Part 2

milestone = 100  # ==============================
# Powers of B have been tested, sonext try a few primes.
# The simpler loop skips the trick of stepping by 2 through the odd
# numbers from 3, filtering the further multiples of 3.
m = NUM_TRIALS
for z in [3, 5, 7, 11, 13, 17, 19, 23]:
    test_integer_powers(z, z, 1, m)
if pow_err_cnt > 0:
    print("Errors like this may invalidate financial calculations")
    print("\tinvolving interest rates.")

print_if_err_cnt_positive()
pow_err_cnt += save_pow_err_cnt
if pow_err_cnt == 0:
    print("... no discrepancies found.")
if pow_err_cnt > 0:
    pause()
else:
    print("")

Part 3