Recall & Review
beginner
What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
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intermediate
Why do we only check divisors up to the square root of a number when testing for primality?
Because if a number n is divisible by a number greater than its square root, it must also be divisible by a number smaller than the square root. So checking up to the square root is enough.
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beginner
What is the simplest method to check if a number is prime?
Try dividing the number by all integers from 2 up to the square root of the number. If none divide evenly, the number is prime.
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beginner
What should you return if the number is less than 2 in a prime check function?
Return false because numbers less than 2 are not prime by definition.
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beginner
In C, which data type is best to use for the number when checking primality?
Use an integer type like int or long depending on the range of numbers you want to check.
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Which number is NOT a prime number?
✗ Incorrect
4 is not prime because it can be divided evenly by 2.
What is the smallest prime number?
✗ Incorrect
2 is the smallest prime number.
When checking if 29 is prime, up to which number should you check for divisors?
✗ Incorrect
Check divisors up to the square root of 29, which is approximately 5.38, so check up to 5.
If a number is divisible by 1 and itself only, it is:
✗ Incorrect
Prime numbers have only 1 and themselves as divisors.
Which of these is an efficient way to check primality?
✗ Incorrect
Checking up to the square root of n is efficient and sufficient.
Explain how to check if a number is prime using a simple algorithm.
Think about dividing the number by smaller numbers.
You got /4 concepts.
Why is it enough to check divisors only up to the square root of the number when testing primality?
Consider how multiplication pairs work.
You got /3 concepts.