# Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
#
# 2^2=4, 2^3=8, 2^4=16, 2^5=32
# 3^2=9, 3^3=27, 3^4=81, 3^5=243
# 4^2=16, 4^3=64, 4^4=256, 4^5=1024
# 5^2=25, 5^3=125, 5^4=625, 5^5=3125
# If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
#
# 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
#
# How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?


def list_distinct_primes(x):
    distinct_primes = set()  # we use a set because we care about duplicates, but not about order

    for i in range(2, x + 1):
        for j in range(2, x + 1):
            distinct_primes.add(i ** j)

    return distinct_primes  # brute force works very quickly


print(len(list_distinct_primes(100)))  # 9183
