# Re: How many Prime numbers

*From*: "Tim Peters" <tim.one@xxxxxxxxxxx>*Date*: Tue, 3 Oct 2006 17:25:44 -0400

[L]

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.

[Tim Peters]

Nobody knows, exactly, and nobody is likely to know for many years

to come:

http://primes.utm.edu/howmany.shtml

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:

http://numbers.computation.free.fr/Constants/Primes/Pix/results.html

[L]

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 ;-)

.

**References**:**How many Prime numbers***From:*L

**Re: How many Prime numbers***From:*Tim Peters

**Re: How many Prime numbers***From:*L

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