
theorem
  2833 is prime
proof
  now
    2833 = 2*1416 + 1; hence not 2 divides 2833 by NAT_4:9;
    2833 = 3*944 + 1; hence not 3 divides 2833 by NAT_4:9;
    2833 = 5*566 + 3; hence not 5 divides 2833 by NAT_4:9;
    2833 = 7*404 + 5; hence not 7 divides 2833 by NAT_4:9;
    2833 = 11*257 + 6; hence not 11 divides 2833 by NAT_4:9;
    2833 = 13*217 + 12; hence not 13 divides 2833 by NAT_4:9;
    2833 = 17*166 + 11; hence not 17 divides 2833 by NAT_4:9;
    2833 = 19*149 + 2; hence not 19 divides 2833 by NAT_4:9;
    2833 = 23*123 + 4; hence not 23 divides 2833 by NAT_4:9;
    2833 = 29*97 + 20; hence not 29 divides 2833 by NAT_4:9;
    2833 = 31*91 + 12; hence not 31 divides 2833 by NAT_4:9;
    2833 = 37*76 + 21; hence not 37 divides 2833 by NAT_4:9;
    2833 = 41*69 + 4; hence not 41 divides 2833 by NAT_4:9;
    2833 = 43*65 + 38; hence not 43 divides 2833 by NAT_4:9;
    2833 = 47*60 + 13; hence not 47 divides 2833 by NAT_4:9;
    2833 = 53*53 + 24; hence not 53 divides 2833 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2833 & n is prime
  holds not n divides 2833 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
