Re: Is this proof of infinitely many primes flawed?

In article
<192daabf-10e1-483f-bab3-df686a5390ae@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
conrad <conrad@xxxxxxxxxx> wrote:

Suppose p_1,p_2,...,p_n are all the primes

Let M = (p_1,p_2,...,p_n) + 1

Suppose p_k | M

Clearly p_k | (p_1,p_2,...,p_n)

then p_k | M - (p_1,p_2,...,p_n) = 1

But p_k > 1 (Contradiction)

Where I do not follow this proof is
if we suppose p_k divides evenly M
then how can we say p_k divides
evenly (p_1,p_2,...,p_n)?

It has nothing to do with assuming p_k | M. It is simply obvious, as
obvious as saying 5 | 3*5*7.

What's the reasoning behind that?

--
conrad
.

Relevant Pages
Loading