#Incorrect statement in the Proof by Contradiction description

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north pagoda
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It states "...multiply all primes and add 1, the result would be also be prime"
That statement is not true, what is true is that the resulting number is not divisible by any of the initial primes, so there will be a larger prime factor. A counter-example to the statement is:
2⋅3⋅5⋅7⋅11⋅13+1=30031 = 59*509

Also there's a typo "would be also be prime" -> "would also be prime",