import math, time
 
def sieve_of_eratosthene(N):
 
    # Cria-se uma lista referente a todos os inteiros entre 0 e N:
    A = [True] * (N+1)
 
    # Define os números 0 e 1 como não primos:
    A[0] = A[1] = False
 
    # Percorra a lista até encontrar o primeiro número primo:
    for value, prime in enumerate(A):
 
        # O número é primo?
        if prime:
 
            # Retorna o número primo:
            yield value
 
            # Remova da lista todos os múltiplos do número enontrado:
            for i in range(value**2, N+1, value):
                A[i] = False
 
start = time.time()
 
# Percorre a lista de números primos menores que N:
for prime in sieve_of_eratosthene(500):
 
    # Calcula o valor de n que define o Pn:
    n = math.log2(prime+1)
 
    # Verifica se n é inteiro, sendo um primo de Mersenne:
    is_mersenne = n.is_integer()
 
    # Se for um primo de Mersenne, calcula o número perfeito:
    if is_mersenne:
        print(2**(n-1) * prime)
 
print('Tempo de execução: ' + str(time.time() - start) + 's')

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