Thread: prime numbers

Following Euclid's proof that there are infinitely many primes, and starting the list with 5 and 7, you form the number 5*7+1=36, and you get the new prime numbers 2 and 3 because 36=2*2*3*3. Which new prime numbers would you get if your starting list were the following?

a. 2,3,5

b. 2,3,5,7

c. 3,5

Originally Posted by ihavvaquestion

Following Euclid's proof that there are infinitely many primes, and starting the list with 5 and 7, you form the number 5*7+1=36, and you get the new prime numbers 2 and 3 because 36=2*2*3*3. Which new prime numbers would you get if your starting list were the following?

a. 2,3,5

b. 2,3,5,7

c. 3,5

c. 3*5+1=16. Now what are the prime factors of 16?

3*5+1+16=2*2*2*2=16, so 2 is the only new prime number?

a. 2*3*5+1=31, so is 31 the only new prime number?

b. 2*3*5*7+1=211, so is 211 the only new prime number?

Originally Posted by ihavvaquestion

3*5+1+16=2*2*2*2=16, so 2 is the only new prime number?

a. 2*3*5+1=31, so is 31 the only new prime number?

b. 2*3*5*7+1=211, so is 211 the only new prime number?

Correct!