Target and hashing question

Hi, question about the target, nonce and POW.

Lets say the target is = 238,348 * 2^176 = 0x0000000000000003A30C00000000000000000000000000000000000000000000 = 22,829,202,948,393,929,850,749,706,076,701,368,331,072,452,018,388,575,715,328

The total space for 256 bits is = 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,935

So, if I can produce 1 trillion hashes a second (1,000,000,000,000), then worst case scenario it would take me this many days:
256bit space - target = (Number of hashes ABOVE target) / 1,000,000,000,000 (hashing rate) / 3600 (min in hour) / 24 (hour in day)

Did I do this right? Now, the book Mastering Bitcoin says on average it would take 59 days...how did he get that number? I didn't get anywhere near that number. Also, how do you take the average in this space? What does he mean average? I know bitcoin picks a target that is always 10 minutes, but lets forget about that for a moment and work with the numbers above.

What am I doing wrong?