Please give a a reason, why 1 is a composite

[Hans Aberg]

> On 25 Mar 2015, at 20:20, tg at gmplib.org wrote:
> 
> Vincent Lefevre <vincent at vinc17.net> writes:
> 
>  On 2015-03-25 08:45:53 +0100, tg at gmplib.org wrote:
>> There are texts (older ones more than modern ones) that define 1 to be
>> prime.  The common view today is that it is not prime (and certainly not
>> a composite).
> 
>  I agree, but this is not what the GMP 6.0.0 manual says:
> 
>   -- Function: int mpz_probab_prime_p (const mpz_t N, int REPS)
>       Determine whether N is prime.  Return 2 if N is definitely prime,
>       return 1 if N is probably prime (without being certain), or return
>       0 if N is definitely composite.
> 
>  which implies that a number is either prime or composite. This is wrong!

There are mutually exclusive sets: zero-divisors (0 in an integral domain), units, composites, and primes.