Re: How many Prime numbers
- From: "Tim Peters" <tim.one@xxxxxxxxxxx>
- Date: Tue, 3 Oct 2006 17:25:44 -0400
I have been trying to find out how many prime numbers there are in 2 to
128 power. I am sure this number is available somewhere but I have
been luckless in finding it.
Nobody knows, exactly, and nobody is likely to know for many years
AFAIK, it's still the case that the largest n for which pi(n) is known
exactly is n = 4*10^22 (your 2^128 ~= 3.4*10^38, much larger). That took
about 250 CPU-days to compute using the fastest known algorithm:
I assume that means a 128 bit code is almost fool (poor choice) proof.
Sorry, I don't know what you mean by "a 128 bit code". The exact number of
primes <= n isn't relevant to any codes I'm aware of. Any system relying
on, e.g., that it's difficult to /factor/ 128-bit integers is worthless,
because modern methods can factor integers of that size quickly. But I
don't know if that's relevant to what you intended to ask ;-)