Prime Numbers Quiz

Play an AI-generated podcast conversation about this lesson

What is a prime number?

A number greater than 1 that is not prime
A number that is a product of two smaller natural numbers
A number that is not a product of two smaller natural numbers (correct)
A number that is divisible by 1 and itself

Why is 5 considered a prime number?

It is divisible by 1 and itself
It is a product of two smaller natural numbers
It is larger than 1
It can only be written as a product involving 5 itself (correct)

Why is 4 considered a composite number?

It is not a product of two smaller natural numbers (correct)
It can only be written as a product involving 4 itself
It is not larger than 1
It is a prime number

What is the fundamental theorem of arithmetic?

Every natural number greater than 1 is either a prime itself or can be factorized as a product of primes (A) Signup and view all the answers

What is the property of being prime called?

Primality (D) Signup and view all the answers

Match the following primality tests with their descriptions:

Trial division = Checks whether n is a multiple of any integer between 2 and $\sqrt{n}$ Miller-Rabin primality test = Fast but has a small chance of error AKS primality test = Always produces the correct answer in polynomial time but is too slow to be practical Mersenne numbers = Numbers for which particularly fast primality testing methods are available Signup and view all the answers

Match the following terms with their definitions:

Prime number = A natural number greater than 1 that is not a product of two smaller natural numbers Composite number = A natural number greater than 1 that is not prime Primality = The property of being prime Fundamental theorem of arithmetic = Every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order Signup and view all the answers

Match the following numbers with their classifications:

5 = Prime 4 = Composite 24,862,048 = Mersenne prime 2 = Prime Signup and view all the answers

Match the following descriptions with their corresponding numbers:

Number divisible only by 1 or itself = Prime number A product (2 × 2) in which both numbers are smaller than 4 = Composite number Natural number greater than 1 that is not prime = Composite number Number for which particularly fast primality testing methods are available = Mersenne numbers Signup and view all the answers

Match the following statements with their corresponding numbers:

5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself = 5 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4 = 4 The largest known prime number as of December 2018 is a Mersenne prime with 24,862,048 decimal digits = 24,862,048 Every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order = Fundamental theorem of arithmetic Signup and view all the answers