> with(numtheory):
Warning, the protected name order has been redefined and unprotected
> n:=1234567;
                          n := 1234567
> k:=987;
                            k := 987
> r:=irem(n,k,'q');
                            r := 817
> q;
                              1250
> n mod k;
                              817
> ifactor(n);
                          (127) (9721)
> isprime(n);
                             false
> S:={2}:
> for n from 3 to 200 by 2 do
> if isprime(n) then S:=S union {n}:
> end if:
> end do: 
> S;
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 

  73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 

  157, 163, 167, 173, 179, 181, 191, 193, 197, 199}
> n_primes:=nops(S);
                         n_primes := 46
> S:=S minus {2};
S := {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 

  73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 

  157, 163, 167, 173, 179, 181, 191, 193, 197, 199}
> S1:={}: S2:={}:
> for p in S do
> if p mod 4 = 1 then S1:=S1 union {p}
> else S2:=S2 union {p}
> end if:
> end do:
> nops(S1);
                               21
> nops(S2);
                               24
> #################
> p:=11:
> a:=2:
> a&^(p-1) mod p;
                               1
> order(a,p);
                               10
> b:=3;
                             b := 3
> order(b,p);
                               5
> b&^5 mod p;
                               1
>