Question

Prove this theorem:
There is infinitely many prime numbers.

Answer 1

to prove this its very easy as long as numbers never end the prime numbers will be infinitve

Answer 2

hope this helps

Answer 3

Assume a finite number of primes p,p1,p2,p3.....pn.

Derive a contradiction.

Answer 4

proof by contradiction.
suppose there are finitely many.
then list them, say they are
\[p_1,p_2,...,p_n\] and consider the number
\[m=p_1\times p_2\times ...\times p_n+1\]
it clearly leaves a remainder of 1 when divided by each prime,
so it is either prime or divisible by some larger prime not in the list.

Answer 5

euclid, 300 b.c.

Answer 6

thanks :)