Understanding Wilson Primes

The video tutorial discusses the concept of primes, focusing on Wilson primes, a special category of primes. It explains Wilson's theorem, which states that for any prime number P, (P-1)! + 1 is divisible by P. The video demonstrates this theorem with examples and highlights that Wilson primes are unique because they pass the test twice. The tutorial also covers the limitations of using Wilson's theorem for testing primes due to the complexity of calculating factorials. Finally, it introduces the Wilson lemma, emphasizing the uniqueness of Wilson primes.

What is a Wilson prime?

• A prime number that is also a perfect square

• A prime number that satisfies Wilson's theorem twice

• A composite number that satisfies Wilson's theorem

• A prime number that is less than 10

According to Wilson's theorem, what is true for any prime number P?

• (P-1)! + 1 is divisible by P

• (P+1)! + 1 is divisible by P

• (P-1)! - 1 is divisible by P

• (P+1)! - 1 is divisible by P

In the example of Wilson's theorem with the prime number 5, what is the result of (5-1)! + 1?

• 23

• 24

• 25

• 26

Why do composite numbers fail Wilson's theorem?

• They are not prime numbers

• Their factorial plus one is not divisible by the number

• They are always even numbers

• They are not divisible by their factorial

What makes Wilson primes unique compared to other primes?

• They are the only primes that are even

• They satisfy Wilson's theorem twice

• They are the largest known primes

• They are the only primes less than 100

Which of the following is NOT a Wilson prime?

• 7

• 563

• 5

• 13

What is the factorial of 6 used in the example with the number 7?

• 720

• 5040

• 120

• 24

What happens when you apply Wilson's theorem to the number 7?

• It satisfies the theorem once but fails the second time

• It satisfies the theorem twice

• It does not satisfy the theorem at all

• It satisfies the theorem three times

What is the significance of Wilson's theorem in testing for primes?

• It is only applicable to even numbers

• It is only applicable to numbers less than 10

• It is a quick and efficient test for primes

• It is a 100% accurate test for primes but not efficient

Why is Wilson's theorem not practical for large numbers?

• It is not accurate for large numbers

• It requires calculating large factorials

• It requires complex mathematical tools

• It only works for small primes