3. Prime Numbers

Infinitude Of Primes — Quiz

Test your understanding of infinitude of primes with 5 practice questions.

Practice Questions

Question 1

What does the infinitude of primes theorem say?

Question 2

In Euclid's proof, suppose $N=2\cdot3\cdot5+1$. What is the remainder when $N$ is divided by $2$, $3$, or $5$?

Question 3

Why does the number $N=p_1p_2\cdots p_n+1$ not have any of the primes $p_1, p_2, \dots, p_n$ as a divisor?

Question 4

What contradiction appears if $p_1, p_2, \dots, p_n$ are claimed to be all the primes?

Question 5

Which fact about integers is used to guarantee that $N$ has a prime factor?