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. in matlab