6. On the blackboard, there are numbers 1 and 2. It is stipulated that new numbers can be written according to the following method: If there are numbers $a$ and $b$ on the blackboard, then the number $a b + a + b$ can be written. Using this method, can the following numbers be obtained:
(a) Number 131213
(b) Number 12131
Let the new number $ab + a + b$ be $c$. This means $c + 1 = ab + a + b + 1 = (a + 1)(b + 1)$. This implies that if the number written on the blackboard is replaced by a number that is 1 greater, then each new number will be the product of two existing numbers. Starting with the numbers 2 and 3, after several multiplications, we will get a number of the form $2^n \cdot 3^m$, where $n, m$ are natural numbers. Clearly, all such numbers can be obtained. This means that in the original situation, only numbers of the form $2^n \cdot 3^n - 1$ can be obtained. The number 13121 is of this form, while 12131 is not.