https://twitter.com/mnaeraxr/status/1504102233276878852

brute.py

for j in range(1, 100):
    for i in range(1, 100):
        b = i**j
        b_s, i_s, j_s = map(str, (b, i, j))
        if b_s.startswith('1') and b_s.endswith(i_s + j_s):
            x = b_s[1:-len(i_s + j_s)]
            print(f"{b} = 1^{x} * {i}^{j}")

complex.py

def estimate_digit(a, b):
    num_digits = 1
    start = 1.

    for _ in range(b):
        start *= a
        while start > 10**6:
            start /= 10
            num_digits += 1

    while start >= 10:
        start /= 10
        num_digits += 1
    return int(start), num_digits


for a in range(1, 10000):
    for b in range(1, 10000):
        suffix = str(a) + str(b)
        
        fin = pow(a, b, 10**len(suffix))
        
        if suffix == str(fin):
            first_digit, num_digits = estimate_digit(a, b)

            if first_digit == 1:
                print(a, b, suffix, num_digits)