music_math_raffle.py

#!/usr/bin/env python3
"""
Solution for https://scrap.tf/raffles/2JKVYD
"""

# https://github.com/savoirfairelinux/num2words
from num2words import num2words

PRIMES = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 
    61, 67, 71, 73, 79, 83, 89, 97]

# The pi function returns the number of primes below x, this is a lookup table
# for a few results
PI_LOOKUP = {
    2357947691: 114870774,
    25937424601: 1131108518,
    10604499373: 481269293,
    137858491849: 5602858280,
    6975757441: 322734457,
    118587876497: 4849395783
}

def format_num(num):
    num_str = num2words(num)
    # Replace some stuff to make the format as required
    num_str = num_str.replace(", ", " ").replace("-", " ").replace(" and", "").title()
    return num_str

start = PRIMES.index(7)+1
powers = set()
# Loop over primes between 11 and 29 (just an arbitrary limit)
for x in PRIMES[start:10]:
    # Loop over numbers between 0 and 20 (arbitrary as well)
    for y in range(0,20):
        power = x ** y
        # Check if the number is between the 100 millionth and 10 billionth prime
        # (range of numers with ~14 words)
        if 2038074743 < power < 252097800623:
            powers.add(power)
            print(x, y, power)
print()

# I manually filled in PI_LOOKUP from https://primes.utm.edu/nthprime/index.php
# because there wasn't enough time left to write a parser for a list or website
for power in powers:
    if power not in PI_LOOKUP:
        continue
    # Get the number of primes below the power from the lookup table
    num_primes = PI_LOOKUP[power]
    # Format the number as words
    num_str = format_num(num_primes)
    # Check if the string has 14 words
    if len(num_str.split()) == 14:
        print(power, num_str)