> with(numtheory):
> n:=1234567;
                          n := 1234567
> isprime(n);
                             false
> for a from 2 to n-1 while a&^(n-1) mod n = 1 do
> end do:
> a;
                               2
> a&^(n-1) mod n;
                             899557
> ## o n legetai pseudoprwtos ws pros th bash a an (a,n)=1 kai a^(n-1) mod n =1
> 
> fermat_witness:=proc(n,a)
> if igcd(a,n)=1 and a&^(n-1) mod n<>1 then RETURN(1)
> else RETURN(0) 
> end if:
> end proc:
> 
> ## o n legetai ari8mos tou Carmichael an einai pseudoprwtos ws pros
> ## ka8e bash 2 <= a <= n-1 me (a,n)=1 kai den einai prwtos
> 
> is_carmichael:=proc(n)
> local a:
> for a from 2 to n-1 do
> if fermat_witness(n,a)=1 then RETURN(0)
> end if:
> end do:
> RETURN(1):
> end proc:
> 
> S:={};

                            S := {}
> for n from 3 to 2000 do
> if is_carmichael(n)=1 then S:=S union {n}
> end if:
> end do:
> 
> P:={};
                            P := {}
> for n from 3 to 2000 do
> if isprime(n) then P:= P union {n}
> end if:
> end do:
> S minus P;
                       {561, 1105, 1729}
>