FTA: “For example, one of the oldest results in math is Euclid’s proof from 300 BCE that there are infinitely many prime numbers. It begins with the recognition that you can always find a new prime by multiplying all known primes and adding 1”
So, if all the primes you know are 5 and 7, you can find a new one by computing 5×7+1? ;-)
This is a very common error. The claim doesn’t even hold if you know the first n primes. The first counterexample is 2×3×5×7×11×13+1=59×509. All you can tell is that the result has at least one prime factor that’s not yet in your list.
So, if all the primes you know are 5 and 7, you can find a new one by computing 5×7+1? ;-)
This is a very common error. The claim doesn’t even hold if you know the first n primes. The first counterexample is 2×3×5×7×11×13+1=59×509. All you can tell is that the result has at least one prime factor that’s not yet in your list.