Understanding Prime Numbers and Goldbach's Conjecture

The video explores the prime factorization of 210, highlighting its unique property as a sum of two primes in multiple ways. It delves into the nature of prime numbers, Goldbach's Conjecture, and the significance of 210 in this context. The video concludes with a proof of 210's special status and mentions the mathematicians who contributed to this discovery.

What is the prime factorization of the number 210?

• 2 x 3 x 7 x 11

• 3 x 5 x 7 x 11

• 2 x 3 x 5 x 7

• 2 x 3 x 5 x 11

Which of the following is NOT a prime number?

• 5

• 9

• 7

• 2

What is a unique property of prime numbers greater than 2?

• They are all less than 10

• They are all divisible by 2

• They are all odd

• They are all even

What does Goldbach's Conjecture propose?

• Every odd number is the sum of two primes

• Every even number greater than 2 is the sum of two primes

• Every even number is the sum of two even numbers

• Every prime number is the sum of two even numbers

Why is Goldbach's Conjecture significant in number theory?

• It has been proven for all numbers

• It was proven by Euclid

• It remains unproven and is a major unsolved problem

• It only applies to numbers less than 100

What makes the number 210 special in the context of Goldbach's Conjecture?

• It is the only number that is a product of three primes

• It is the only number that is both even and odd

• It is the smallest number that cannot be expressed as a sum of two primes

• It is the largest number that can be expressed as a sum of two primes in multiple ways

What is the significance of the number 105 in the context of 210 and Goldbach's Conjecture?

• It is the sum of two prime numbers

• It is half of 210 and helps determine prime pairs

• It is the smallest prime number greater than 210

• It is the largest prime number less than 210

Who were the mathematicians that proved the unique property of 210 in 1993?

• Leonhard Euler and Carl Gauss

• Jean-Marc Deshouillers, Andrew Granville, Wladyslaw Narkiewicz, and Carl Pomerance

• Euclid and Pythagoras

• Isaac Newton and Albert Einstein

What is the term used by Brady to describe the number 210?

• Very Even

• Very Unique

• Very Goldbach-y

• Very Prime

What is the last number for which the unique property related to Goldbach's Conjecture holds?

• 100

• 210

• 300

• 400