In article <XnsA218A398ABCFEgoddardbenetscapenet@18.104.22.168>, Bart Goddard <firstname.lastname@example.org> wrote:
> Sandy <email@example.com> wrote in > news:_I6dnb4o3esENZvPnZ2dnUVZ8sqdnZ2d@bt.com: > > > But suppose we leave the OPs second alternative to one side and ask > > 'Is there any way to combine 2 primes to get a larger prime?' Given > > the enormous number of ways two numbers can be "combined" to yield a > > third, it would seem to be a hopeless task to give a negative answer. > > Indeed. E.g., let p and q be two distinct primes. Use the Euclidean > algorithm to express their gcd as a linear combination of p and q, > say, ap + bq =1. Multiply by 3 to get 3ap + 3bq =3, which is a prime. > We have now combined two primes to obtain a third. So much for > another crackpot's "resoundingly" false assertions.
Does not work if one of the original two primes is 3.