[Cryptography] 1023 nails in the coffin of 1024 RSA...
John Denker
jsd at av8n.com
Tue Oct 7 15:21:29 EDT 2014
On 10/07/2014 04:14 AM, Jerry Leichter wrote:
> N/ln N is just an approximation. For all you know,
> the true number of primes could be only a millionth of that!
I wouldn't have said that.
Actually
π(N) > N / (2 + ln N) [1]
is a hard lower bound for all N ≥ 2, i.e. for all nontrivial N.
Even tighter bounds exist, but [1] is more than good enough
for present purposes.
Reference:
http://en.wikipedia.org/wiki/Prime_number_theorem#Bounds_on_the_prime-counting_function
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