Problem 239

Twenty-two Foolish Primes

A set of disks numbered 1 through 100 are placed in a line in random order.

What is the probability that we have a partial derangement such that exactly 22 prime number discs are found away from their natural positions?
(Any number of non-prime disks may also be found in or out of their natural positions.)

Give your answer rounded to 12 places behind the decimal point in the form 0.abcdefghijkl.

二十二个愚蠢素数

将一系列标有1至100的盘子按随机顺序排成一排。

在这个重排中有恰好22个素数不在原位上的概率是多少？
（并不要求任意非素数盘子是否在原位上。）

将你的答案四舍五入至小数点后12位小数，即格式为0.abcdefghijkl。