Question

Prove that there is no largest prime numbers

Answer 1

Answer:

i saw an example where it is proved with contradiction.(Idea is basically that of Euclid's proof)

Imagine that the largest prime prime is 13.So, total number of primes we know are-2,3,5,7,11,13.

Now,if I do (2×3×5×7×11×13)+1=30031.So, we can see that 30031 is not divisible by 2,3,5,7,11,13 as they leave remainder 1. Also,as it is formed by multiplying only primes it does not have any other composite factors.We also see that 30031=59×509.Which are again two primes.Thus,13 is not the largest prime.