When y=0, -x2+x+2=0 means -(x-2)(x+ 1)=0,

X=2 or x=- 1.

So let P(x, y) (2 > x > 0, y > 0),

∴c=2(x+y)=2(x-x2+x+2)=-2(x- 1)2+6.

When x= 1, the maximum value of c =6.

That is, the maximum circumference of the quadrilateral OAPB is 6.

So the answer is: 6.