Reports

Just use recursion and cache. Python has the decoration @lru_cache, which autoimplements caching to a recursive function. Runs in 2.304 seconds

The function should look something like:

from functools import lru_cache

@lru_cache(maxsize=None)
def collatz(x):
    if x == 1:
        return 1
    
    if x % 2 == 0:
        return 1 + collatz(x // 2)
    
    return 1 + collatz(3*x + 1)

if you want to do it without the decoration:

cache = {}
def collatz(x):
    global cache
    
    if x in cache:
        return cache[x]
    
    if x == 1:
        return 1
    
    if x % 2 == 0:
        result = 1 + collatz(x // 2)
    else:
        result = 1 + collatz(3*x + 1)
    
    cache[x] = result
    return result

here's the main code:

maxChain = 0
maxNumber = 0
for i in range(1, 1000001):
    chainSize = collatz(i)
    
    if chainSize > maxChain:
        maxChain = chainSize
        maxNumber = i
    
print(maxNumber)

79504206