Understanding Prime Numbers and Their Properties

The video explores prime numbers, their properties, and how to identify them. It covers prime factorization, the fundamental theorem of arithmetic, and methods to check for primality, including the sieve of Eratosthenes. The video also shares interesting facts and theorems about primes.

What is the smallest prime number?

• 1

• 3

• 2

• 4

Which of the following numbers is not prime?

• 2

• 3

• 4

• 5

What is the prime factorization of 9?

• 3 x 3

• 2 x 4

• 1 x 9

• 3 x 1

Which rule helps determine if a number is divisible by 3?

• The number ends in 0 or 5

• The sum of the digits is divisible by 3

• The number is even

• The number is a multiple of 10

According to the Fundamental Theorem of Arithmetic, every integer greater than one can be uniquely expressed as:

• A product of primes

• A quotient of primes

• A sum of primes

• A difference of primes

What does the theorem on prime divisors state about a composite number?

• It is only divisible by 1 and itself

• It has no prime divisors

• It has a prime divisor less than or equal to its square root

• It has a prime divisor greater than itself

How can you determine if 539 is a composite number using the theorem discussed?

• Check divisibility by all numbers up to 539

• Check divisibility by all primes up to the square root of 539

• Check divisibility by 2 only

• Check divisibility by 1 and 539 only

What is the purpose of the Sieve of Eratosthenes?

• To factorize composite numbers

• To find the least common multiple

• To find all prime numbers up to a certain integer

• To find the greatest common divisor

Which mathematician proved that there are an infinite number of primes?

• Pythagoras

• Euclid

• Newton

• Archimedes