Let L(N) = exp((ln N)(ln ln N)) as usual. Suppose that a computer does one billi

Question

Let L(N) = exp((ln N)(ln ln N)) as usual. Suppose that a computer does one billion operations per second. (

a) How many seconds does it take to perform L(2100) operations?

(b) How many hours does it take to perform L(2250) operations?

(c) How many days does it take to perform L(2350) operations?

(d) How many years does it take to perform L(2500) operations?

(e) How many years does it take to perform L(2750) operations?

(f) How many years does it take to perform L(21000) operations?

(g) How many years does it take to perform L(22000) operations?

(For simplicity, you may assume that there are 365.25 days in a year.)

Explanation / Answer

(a) 0.0278s
(b) 9552s = 2h39'
(c) 7.1*10^6 = 82d 4h
(d) 3.57*10^10 = 1129y
(e) 5.8*10^15 = 1.8*10^8 y
(f) 1.75*10^20 = 5.5*10^12 y
(g) 3.1*10^34 = 9.8*10^26 y

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