回複：我女兒的題目

Define "derived" member of N: i is derived if exist j that f(j) = i

Define "prime" member of N: i is not derived member of N.

for each prime member i, define prime series x(i): x(i,0) = i, x(i, j) = f(x(i, j-1)). i.e i, f(i), ff(i), fff(i), etc.

1. Any n in N, n belongs 1 and only 1 prime series. (easy to prove, omit)

2. For any number greater than 2011, they not not first or 2nd number in a prime series vise versa. because ff(i-2011) = i

So, 1 to 2011 fills first 2 place of prime series which can't be.