3 ms·
It's not necessarily a prime bigger than PN as the original proof is about some list of primes, not all primes less than some prime. E.g. 3,5 becomes 16, which
by dpbriggs 4y ago
It's not necessarily a prime bigger than PN as the original proof is about some list of primes, not all primes less than some prime. E.g. 3,5 becomes 16, which is missing 2.
- _kst_ 4y agoApparently I misremembered the details of the proof. I thought that it started with (P1, P2, P3, ..., PN) being a list of all the primes from 2 up to PN. Since (P1 * P2 * ... * PN) + 1 either is prime or has a prime factor not in the list, that prime factor must be greater than PN. Apparently (according to Wikipedia's summary) Euclid started with an arbitrary list of primes, and showed that for any such list there is a prime not in the list. Either method works to show that there are infinitely many primes.