4 ms·
You made an error: p1p2...pn + 1 is not necessarily prime, but none of its prime factors are in {p1, ..., pn}. For example, 15 = 2 * 7 + 1 is not prime, but nei
by tprice7 10y ago
You made an error: p1p2...pn + 1 is not necessarily prime, but none of its prime factors are in {p1, ..., pn}. For example, 15 = 2 * 7 + 1 is not prime, but neither 3 nor 5 are in {2, 7}. I agree with your overall point though.
- daveguy 10y agoAll primes. Not just the primes you choose. The set of the first n primes here would be {2,3,5,7}. The product plus 1 is 235*7+1 = 211 is prime.
- pmiller2 10y agoThe product of the first n primes + 1 is not always prime, though. See https://en.m.wikipedia.org/wiki/Euclid_number https://en.m.wikipedia.org/wiki/Euclid_number
- deleted 10y ago[deleted]
- yen223 10y ago2*3*5*7*11*13 + 1 = 30031 = 59*509 Neither 59 nor 509 is in {2, 3, 5, 7, 11, 13}, so the proof still holds, but the resultant number is not a "prime" number.