%hw5.tex: Homework assignment 5
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\centerline
{
\bf Dr. Z.'s Number Theory Homework assignment 5
}


{\bf 1.} Decide whether the following integers are prime or composite, using
(i) the very stupid way (ii) the stupid way (iii) the OK way

{\bf a.} $99$ {\bf b.} $37$  


{\bf 2.} Decide whether the following integers are prime or composite, using the OK way

{\bf a.} $101$ {\bf b.} $1001$ .

{\bf 3.} Use the sieve of  Eratosthenes to list {\bf all} the prime numbers $\leq 140$.

{\bf 4.} Prove  that there are infinitely many primes.

{\bf 5.} Find, by only using paper-and-pencil the first six terms of the Euclid-Mullin sequence.

{\bf 6.} (Optional, extra credit) A twin-prime-pair is a pair of two prime numbers that differ by $2$.
The first few are $(3,5)$, $(5,7)$, $(11,13)$. Prove that there are infitely many twin-prime pairs.

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