Question

here we go:

Answer 1

that last fuzz at the far right is a "+1", if it isnt too clear.

Answer 2

>>>>>>>>>>>>>>>>>>>GOING>>>>>>>>>>>>>>>>>>

Answer 3

oh wait. that thing clearly leaves a remainder of 1 when it is divided by all the other primes. so either it is the nth prime, or there must be a smaller one right?

Answer 4

what i mean is that the next prime has to be at most that product. it cannot be bigger

Answer 5

lol thats right.

Answer 6

i was so stuck on doing a straightforward proof by contradiction. i didnt even notice that.

Answer 7

because if the next prime is bigger, and that thing leaves a remainder of one when divided by all previous primes, then of course we have a contradiction

Answer 8

whew i thought you were going to stump the band and keep me awake even longer. g'night

Answer 9

lol, get some sleep. i need some too apparently

Answer 10

Eulers proof that there are lots of primes...

Answer 11

Euclid I mean, lol

Answer 12

euler didn't do absolutely everything. there were a few others...