Task $3$: List of prime numbers

Writing down a list of prime numbers $(2,3,5,7,11,13,17,19,23,...)$ we can see that$$the $9$th prime is $23$ and the sum of the prime numbers below $15$ is

$2+3+5+7+11+13=41.$

a$)$ i$)$ What is the $99$th prime number?

ii$)$ And what is the $9999$th prime number?

b$)$ Find the sum of all the prime numbers

i$)$ below $1500?$ii$)$ below $1\mathrm{.}5$ Million?

Hints:

Start writing code that reproduces the examples given in the introduction. Use your

functions from Task $1.$

For parts i$)$ it is possible to nd the solution by brute force testing all numbers up to

the given limit for primality.

For parts ii$)$ you have to improve your algorithms to deal with large numbers. In case

you cannot nd an algorithm which terminates within acceptable time, explain the$$measures you have taken and what options you have tested. What is the range of the$$largest numbers your algorithm can handle?

After submitting the corresponding test for value checking in the CBEM Moodle with

at least one correct value you can download a pdf with additional hints.