AliVali.py

from math import *
import itertools


def count(seq):
    c = 0
    for _ in seq:
        c += 1
    
    return c


def exactlyOne(seq):
    alreadyMet = False
    for val in seq:
        if val:
            if alreadyMet:
                return False
            else:
                alreadyMet = True
    
    return alreadyMet


def Ks(S):
    for a in itertools.count(2):
        b = S - a
        if a > b:
            break
        
        yield (a, b)


def Kp(P):
    for p in itertools.count(2):
        if P % p != 0:
            continue

        q = P // p
        if p >= 100 or p > q:
            break
        
        if q >= 100:
            continue

        yield (p, q)


def pred0S(S):
    return count(Ks(S)) > 1


def pred0(P):
    return count(Kp(P)) > 1


def pred1(S):
    return pred0S(S) and all(pred0(a * b) for (a, b) in Ks(S))


def pred2(P):
    return pred0(P) and \
        exactlyOne(pred1(p + q) for p, q in Kp(P))


def pred3(S):
    return pred1(S) and \
        exactlyOne(pred2(a * b) for a, b in Ks(S))


for S in range(4, 99+99+1):
    if pred3(S):
        print(S)