12. (9 points) The numbers $1,2,3,4, \cdots$ are arranged in the direction indicated by the arrows (as shown in the figure), turning at the positions of $2,3,5,7,10, \cdots$.
(1) If the first turn is at 2, then the number at the 45th turn is $\qquad$ .
(2) Among the natural numbers from 1978 to 2010, the number that is exactly at a turning point is $\qquad$ .
【Answer】By observing the pattern of numbers at the turning points, we can obtain the number at the $n$-th turning point: when $n$ is odd, it is $1+(1+3+5+\cdots+n)=\left(\frac{n+1}{2}\right)^{2}+1$; when $n$ is even, it is $1+2 \times\left(1+2+3+\cdots+\frac{n}{2}\right)=\left(1+\frac{n}{2}\right) \times \frac{n}{2}+1$.
(1) The number at the 45th turning point is $\left(\frac{45+1}{2}\right)^{2}+1=530$.
(2) When $n=89$, the number at the turning point is $\left(\frac{89+1}{2}\right)^{2}+1=2026$; when $n=88$, the number at the turning point is $\left(1+\frac{88}{2}\right) \times \frac{88}{2}+1=1981$; when $n=87$, the number at the turning point is $\left(\frac{87+1}{2}\right)^{2}+1=1937$; therefore, among the numbers 1978 to 2010, the number that is exactly at a turning point is 1981. Hence, the answers are: (1) 530, (2) 1981.