Euclid's proof of infinite primes

For those who don't know, there are infinite primes and this can be proved by Euclid's proof.

For every prime number, by multiplying all the prime numbers before it (inclusive) and adding 1 to the product, the resultant is a bigger prime number.

$(p_1 \times p_2 \times p_3 \times ... \times p_{n-1} \times p_n) + 1=p_x$

My question to everyone is, do you think you could contradict this proof?

#NumberTheory

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Comments

Well, this proof is not necessarily complete. First of all, this is supposed to be a proof by contradiction, so you must first assume you have a finite number of primes and then do what you have done. Secondly, some definitions are in place. We must define prime numbers as only positive integers greater than one. Then the proof is flawless.

Bob Krueger - 7 years, 5 months ago

the result may be a number which is not prime but it must be divisible by primes not in the list.

Pranav Kirsur - 7 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$