exceeding

x

and

x

/

ln

x

approaches 1 as

x

grows without bound.

(Here ln

x

is the natural logarithm of

x

)

Note that ln

x

= 2[(

x

−

1

x

+1

) +

1

3

(

x

−

1

x

+1

)

3

+

1

5

(

x

−

1

x

+1

)

5

+

···

] for

x

>

0

Compute lnx

using the series above as far as you can without getting

overflow issues and use it to estimate the number of primes based on

the Theorem above