Understanding Mersenne Primes and Primality Tests

What is the significance of the newly discovered largest prime number?

• It is the first composite number discovered.

• It is a perfect number.

• It is the smallest known prime number.

• It is a Mersenne prime with over 41 million digits.

What defines a Mersenne prime?

• A prime number that is one more than a power of two.

• A composite number that is one less than a power of two.

• A number that is both prime and composite.

• A prime number that is one less than a power of two.

Why are Mersenne primes easier to verify for primality?

• They are smaller in size.

• They are always composite.

• They are one less than a power of two, simplifying calculations.

• They do not require computational power to verify.

What is the role of the Great Internet Mersenne Prime Search (GIMPS)?

• To find the smallest prime numbers.

• To verify the primality of composite numbers.

• To disprove the existence of Mersenne primes.

• To use distributed computing to find and verify Mersenne primes.

What does the Fermat primality test determine?

• Whether a number is definitely prime.

• Whether a number is a perfect number.

• Whether a number is composite.

• Whether a number is probably prime.

How does the Lucas-Lehmer test confirm a Mersenne prime?

• By adding the digits of the number.

• By verifying if a specific sequence term is a multiple of the Mersenne number.

• By comparing it to known composite numbers.

• By checking if the number is even.

What is a perfect number?

• A number that is both prime and composite.

• A number that is one less than a power of two.

• A number that is equal to the sum of its proper divisors.

• A number that is equal to the sum of its digits.

What did Euclid prove about Mersenne primes?

• They are the smallest prime numbers.

• They are always composite.

• They are unrelated to perfect numbers.

• They can generate perfect numbers.

How are perfect numbers related to Mersenne primes?

• Perfect numbers are unrelated to Mersenne primes.

• Perfect numbers are generated from Mersenne primes.

• Perfect numbers are always larger than Mersenne primes.

• Perfect numbers are smaller than Mersenne primes.

What is the historical significance of Euclid's theorem?

• It disproved the existence of perfect numbers.

• It established a connection between Mersenne primes and perfect numbers.

• It showed that all numbers are prime.

• It proved that Mersenne primes are composite.