- #1

- 757

- 354

If there were a largest prime

you could take the product of all prime factors

add (or take away) 1 and get another large prime (a contradiction)

So what if you search for larger primes this way?

(2,3,5,7,11,13)

(2*3) +-1 = 6 +-1 = {5,7}

(2*3*5) +-1 = 30+-1 = {29.31}

(2*3*5*7)+-1 = 210+-1 = {209,211} (209 is not prime)

(2*3*5*7*11)+-1 = 2310+-1 = {2309,2311}

(2*3*5*7*11*13)+-1 = 30030+-1={30029,30031} (30031 is not prime)

I have two questions:

Do prime numbers of this sort have a special name? (like Marsenne primes are (powers of 2) +-1?)

Are there infinitely many of them?

This was just an odd thought I had. You can keep going and find products where neither one above or one below is a prime.