Code

import math
import time

start = time.time()

def f(n):
    c = 1
    Min1 = -1
    Min2 = -1
    sqrt = n**0.5
    e = n % 2 == 1

    if e:
        c += 1
    if e and (sqrt != int(sqrt) or sqrt % 2 != 1):
        return

    sqrt = int(sqrt)
    if e:
        c += 1
        for a in range(3, math.ceil(sqrt), 2):
            if n % a == 0:
                c += 2
                if Min1 == -1:
                    Min1 = a

            if c > 5:
                return

    else:
        for a in range(2, sqrt + 1):
            if n % a == 0:
                j = n // a
                if j % 2 == 1:
                    c += 1
                    if Min1 == -1:
                        Min1 = j
                elif a % 2 == 1:
                    c += 1
                    if Min2 == -1:
                        Min2 = a
            if c > 5:
                return

    if c == 5:
        if Min1 == -1:
            Min1 = 88_888_889
        if Min2 == -1:
            Min2 = 88_888_889

        print(n, min(Min1, Min2))

for i in range(77_777_777, 88_888_888 + 1):
    f(i)

print(time.time() - start)