2. $A B$ is a chord of $\odot O$, $P$ is a point outside $\odot O$, $P B$ is tangent to $\odot O$ at $B$, $P A$ intersects $\odot O$ at $C$, and $A C = B C$, $P D \perp A B$ at $D$, $E$ is the midpoint of $A B$, $D E = 1000$. Then $P B=$
2.2000 .

As shown in Figure 5, take the midpoint $F$ of $PA$, and connect $DF$, $EF$. Then $EF \parallel PB$. Also, $DF = \frac{1}{2} PA$, so $DF = AF$. Since $AC = BC$, $\triangle AFD$ is an isosceles triangle. Therefore, $\angle 2 = \angle 4 = \angle 1$. Since $EF \parallel PB$ and $DF \parallel BC$, $\angle 3 = \angle 5$. From the fact that $PB$ is a tangent, we know $\angle 5 = \angle 2$. Thus, $\angle 3 = \angle 4$, and $DE = L_i$, which means $PB = 2EF = 2DE = 2000$.