Prime Numbers and Python Functions Quiz

Why are prime numbers considered important in number theory?

• They are the largest numbers.

• They are the building blocks of whole numbers.

• They are always even.

• They are used in addition.

What is the definition of a prime number?

• A number that is always odd.

• A number that is neither positive nor negative.

• A number divisible by 2 and 3.

• A number divisible only by 1 and itself.

In the first version of the primality test, which numbers are checked as divisors?

• All numbers from 2 to n-1.

• Only odd numbers.

• All numbers from 1 to n.

• Only even numbers.

What optimization is introduced in the second version of the primality test?

• Testing divisors up to the square root of n.

• Testing divisors up to n-1.

• Testing only even numbers.

• Testing only numbers greater than n.

Why is it unnecessary to test divisors beyond the square root of a number?

• Because all numbers are perfect squares.

• Because factors repeat beyond the square root.

• Because numbers larger than the square root are always prime.

• Because it is computationally expensive.

What is the main improvement in the third version of the primality test?

• Checking numbers greater than n.

• Checking only even numbers.

• Skipping even numbers and checking only odd numbers.

• Using a different programming language.

Why is it efficient to skip even numbers when checking for primality?

• Even numbers are always prime.

• Even numbers are never prime except for 2.

• Even numbers are too large.

• Odd numbers are easier to check.

What is the significance of the number 2 in the context of prime numbers?

• It is the smallest odd prime number.

• It is the only even prime number.

• It is the largest prime number.

• It is not a prime number.

What should you explore if you are dealing with extremely large integers in cryptography?

• Pseudo primes.

• Basic multiplication.

• Basic arithmetic operations.

• Simple addition and subtraction.

What is the purpose of the optimizations discussed in the video?

• To make the code more complex.

• To improve the speed and efficiency of the primality test.

• To make the function harder to understand.

• To increase the number of lines of code.