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A comment on Reasons Why Job Seekers Are Not Given Feedback. Parent comment

Re:Reasons Why Job Seekers Are Not Given Feedback by edu on Friday December 20, 2019 @07:17AM (#21843562)
The parent said to multiply _only the primes_ from 2 to N, and then add one not factorial plus one.

In your example it would be (2 * 3) + 1 = 7, prime.

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Re:Reasons Why Job Seekers Are Not Given Feedback by cion on Friday December 20, 2019 @07:46AM (#21843736)
Oh, sorry, didn't realize that. It still doesn't work, though, as the example of 2 * 3 * 5 * 7 * 11 * 13 + 1 = 59 * 509 shows.
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Re:Reasons Why Job Seekers Are Not Given Feedback by michaelt on Friday December 20, 2019 @08:34AM (#21843970)
Right, but if you were testing N=13 as the highest prime, then (2 * 3 * 5 * 7 * 11 * 13) + 1 must either be prime itself, i.e. have no prime factors, or must have a prime factor greater than 13. And in either case, a prime greater than 13 exists - in your example, 59.

This is Euclid's proof [1] and it's some 2300 years old.

[1] https://en.wikipedia.org/wiki/Euclid%27s_theorem

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Re:Reasons Why Job Seekers Are Not Given Feedback by conanite on Friday December 20, 2019 @08:25AM (#21843925)
It's a little bit more subtle. Assume that there is a finite number of primes, and P is the set of all primes p0, p1, p2... pn. If you multiply all these together and add 1, you have a number Q that's not divisible by any number in P. So P cannot be the set of all primes.
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