Use the Prime Number Theorem to . . . 1. estimate the number of primes between 2127 + 1 and 2128 . 2. estimate the 2128th-largest prime. 3. argue that, roughly, the probability that a randomly chosen...

Use the Prime Number Theorem to . . .

1. estimate the number of primes between 2127 + 1 and 2128 .

2. estimate the 2128th-largest prime.

3. argue that, roughly, the probability that a randomly chosen number close to n is prime is about 1/ ln n. (Hint: what does primes(n) − primes(n − 1) represent?)