3 ms·
> One plus the product of all primes is itself prime One plus the product of the first N primes is not necessarily prime. Consider 2 * 3 * 5 * 7 * 11 * 13 + 1
by dllthomas 10y ago
> One plus the product of all primes is itself prime
One plus the product of the first N primes is not necessarily prime. Consider 2 * 3 * 5 * 7 * 11 * 13 + 1 = 30031 = 59 * 509
- mikeash 10y agoHow about: one plus the product of a list of primes has a prime factor not in the list.
- jwatte 10y agoYes! Because primes are infinite! The statement assumes limited primes. And, because it falsifies, it proves primes must be unlimited. I find this argument based on prime factors much simpler.
- dllthomas 10y agoI would have been fine with "would have to be prime"; I like the edit Mike suggested even better.