Question

Here is one from number theory...
Prove that there are infinitely many primes.....

Answer 1

4p+3 will be a prime for all prime p
lets assume p is the last prime then 4p+3 is also a prime
this contradicts our assumption hence there are infinitly many primes

Answer 2

but how can u tell that 4p+3 is a prime?

Answer 3

as p is prime 4p is multiple of 1,2 4,p if you add three nothing factors out so it is a prime

Answer 4

as for me, i've heard of these proofs:
Euclid's Proof (c. 300 BC)
Furstenberg's Topological Proof (1955)
Goldbach's Proof (1730)
Kummer's Restatement of Euclid's Proof
Filip Saidak's Proof (2005)

Answer 5

Yeah sure

Answer 6

http://openstudy.com/study#/updates/4f29d875e4b049df4e9df1b3

Answer 7

4*13+3 = 55 which is composite
to do your proof, you must create the number formed by multiplying ALL primes less than or equal the presumed last prime. then add 1. this number will be divisible by all smaller primes, but with a remainder of 1. So there must be a bigger prime than the presumed last prime.