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% (C) 2010 by Eugeniy Mikhailov, <evgmik@gmail.com>
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\hw{11}

This homework is {\bf optional}. In case of completion the points will be
added to the total of all homeworks.

General comments: 
\begin{itemize}
	\item Do not forget to run some test cases. 
\end{itemize}


\problem{Problem 1 (15 points max)}
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The prime number is the integer which is divisible only  by 1 and itself.
We exclude 1 from the prime numbers list.

Write a function ``primes\_after'' according to the following specification
\begin{lstlisting} [language=matlab]
function PrimeNumbersList = primes_after(N, M)
\end{lstlisting}
which outputs a {\bf row} vector of M prime numbers starting from N 
(inclusive). N and M are guaranteed to be positive integer number, no checks 
for this are necessary.  Make sure your function follows the specification
above {\bf exactly}.

Examples:
\begin{lstlisting} [language=matlab]
>> primes_after(7,2);
ans=[ 7, 11 ]
>> primes_after(1,2);
ans=[ 2, 3 ]
\end{lstlisting}

In our speed comparison tests, 
$M$ will be in order of a 1000 and $N$ will be a large number something like $10^9$ or even more.

\begin{itemize}
	\item 
		If you do the function right you will get only 5 points.
		I.e. it follows specification and output valid results.
	\item 
		You will get extra 5 points if your algorithm is the fastest in the class.
	\item 
		You will get extra 5  points if your algorithm is faster
		than the instructor one.
	\item 
		We will run the competition during the practice section.
\end{itemize}



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