Hmm, good try, but it's not quite right. Here's a simpler way to get all the numbers divisible by 2, 3, 5, or 7, in a 100-number range, and which I think is eas

Hmm, good try, but it's not quite right. Here's a simpler way to get all the numbers divisible by 2, 3, 5, or 7, in a 100-number range, and which I think is easier to verify that it's correct: numbers_not_divisible_by_2_3_5_7 = [] for i in range(520, 620): is_divisible = False for p in [2, 3, 5, 7]: if i % p == 0: is_divisible = True break if not is_divisible: numbers_not_divisible_by_2_3_5_7.append(i) print(numbers_not_divisible_by_2_3_5_7) print(len(numbers_not_divisible_by_2_3_5_7)) And if you run this code you'll find that it demonstrates a counterexample. Between 520 and 620 there are 25 numbers which are not divisible by 2, 3, 5, or 7: [521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569, 571, 577, 583, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619] You really need to use all the primes from 2 to 13 inclusive to get a limit of 23. And even then I was only able to prove it by brute-forcing up to the primorial of 13, but maybe there's a simpler way.