# Essay on PGP as it is used today

vedaal at nym.hush.com vedaal at nym.hush.com
Wed Jul 24 03:36:36 CEST 2019

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On 7/22/2019 at 7:12 AM, "Robert J. Hansen" <rjh at sixdemonbag.org> wrote:

>Mathematicians have come up with different ways to estimate how
>many
>primes there were under a certain value
...
>The first estimate for π(x) was "x divided by the natural
>logarithm of x".
...
>If we do that same equation for a 2048-bit key, it turns out there
>are
>10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>000 000
>000 000 000 000 000 000 000 different prime numbers that could go
>into it.

=====

not really, for GnuPG keys, but for the default size GnuPG key of 4096, it's actually bigger than the number you quoted above ;-)

For a GnuPG key of 4096, it's only necessary to compute for primes up to 2^2048.

But,

Since GnuPG uses 2 primes only in the 2^2048 size, for a 4096 bit key,
then the amount of primes is actually:

[ (2^2048) / ln(2^2048) ]  -  [ (2^2047) / ln (2^2047) ]  =  1.37 x 10^613

So, not to worry about someone creating a 'database' to crack GnuPG ...

vedaal

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