Searching for numbers = perfect powers

import math

lastNumber = 1024
maxBase = math.ceil(math.sqrt(lastNumber))
maxExponent = math.ceil(math.log2(lastNumber))
numbers = []
bases = []
exponents = []
for number in range(4, lastNumber+1):
    for base in range(2, maxBase+1):
        flag = False;
        for exponent in range(2, maxExponent+1):
            if number == base ** exponent:
                numbers.append(number)
                bases.append(base)
                exponents.append(exponent)
                # The flag will become true, in order to have the chance to break out of the 2nd loop (not only from first)
                flag = True
                break
        if flag == True:
            # With the break-command, we will go out from the outer (2nd) loop, to continue the iteration on 'number'
            break

for i in range(0, len(numbers)):
    print(str(numbers[i]) + " = " + str(bases[i]) + " ^ " + str(exponents[i]))
print()
print("There are " + str(len(numbers)) + " numbers = perfect powers from 4 to " + str(lastNumber) + ".")
percentage = (lastNumber - 3) / len(numbers)
print("With other words, 1 such number in " + str(round(percentage, 2)) + " numbers.")