
theorem
  3557 is prime
proof
  now
    3557 = 2*1778 + 1; hence not 2 divides 3557 by NAT_4:9;
    3557 = 3*1185 + 2; hence not 3 divides 3557 by NAT_4:9;
    3557 = 5*711 + 2; hence not 5 divides 3557 by NAT_4:9;
    3557 = 7*508 + 1; hence not 7 divides 3557 by NAT_4:9;
    3557 = 11*323 + 4; hence not 11 divides 3557 by NAT_4:9;
    3557 = 13*273 + 8; hence not 13 divides 3557 by NAT_4:9;
    3557 = 17*209 + 4; hence not 17 divides 3557 by NAT_4:9;
    3557 = 19*187 + 4; hence not 19 divides 3557 by NAT_4:9;
    3557 = 23*154 + 15; hence not 23 divides 3557 by NAT_4:9;
    3557 = 29*122 + 19; hence not 29 divides 3557 by NAT_4:9;
    3557 = 31*114 + 23; hence not 31 divides 3557 by NAT_4:9;
    3557 = 37*96 + 5; hence not 37 divides 3557 by NAT_4:9;
    3557 = 41*86 + 31; hence not 41 divides 3557 by NAT_4:9;
    3557 = 43*82 + 31; hence not 43 divides 3557 by NAT_4:9;
    3557 = 47*75 + 32; hence not 47 divides 3557 by NAT_4:9;
    3557 = 53*67 + 6; hence not 53 divides 3557 by NAT_4:9;
    3557 = 59*60 + 17; hence not 59 divides 3557 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3557 & n is prime
  holds not n divides 3557 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
