Understanding Perfect Numbers

The video discusses perfect numbers, starting with the historical significance of 8,128, the largest known perfect number in antiquity. It explains what makes a number perfect, using examples like 6, 28, 496, and 8,128, where the sum of divisors equals the number itself. The video highlights that only 47 perfect numbers are known today, with open questions about their infinitude and the existence of odd perfect numbers. The largest known perfect number is nearly 2 million digits long.

What is the smallest perfect number?

• 15

• 10

• 6

• 3

Which of the following numbers is a perfect number?

• 30

• 28

• 10

• 5

What is the sum of the divisors of 6, excluding the number itself?

• 3

• 12

• 9

• 6

Which number is the third perfect number?

• 33550336

• 8128

• 28

• 496

How many perfect numbers were known to the ancient Greeks?

• 2

• 3

• 4

• 5

As of today, how many perfect numbers have been discovered?

• 47

• 50

• 100

• 200

What is an open question regarding perfect numbers?

• If they are all odd

• If there are infinitely many

• If they are all even

• If they are all prime

What is the length of the largest known perfect number in digits?

• 2,000,000

• 1,000,000

• 1,500,000

• 1,791,000

What is unknown about perfect numbers?

• If they are all less than 10,000

• If odd perfect numbers exist

• If they are all even

• If they are all divisible by 2

What is the significance of the number 8,128 in the context of perfect numbers?

• It is the smallest perfect number

• It is an odd perfect number

• It is the largest known perfect number

• It was the largest known perfect number in antiquity