show that there are infinitely many primes of the form 4n-1 (proof)

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In this video I show that there are infinitely many primes of the form 4n-1. Enjoy~
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You are allowed to paraphrase Euclid:

The list of prime numbers is infinite because the lowest divisor greater than 1 of p!+1 must be a prime number greater than p.

apusapus
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How can the product of all primes in the set contain 2? 2 is not for the form 4n-1.

Mehraj_IITKGP