
theorem
  6833 is prime
proof
  now
    6833 = 2*3416 + 1; hence not 2 divides 6833 by NAT_4:9;
    6833 = 3*2277 + 2; hence not 3 divides 6833 by NAT_4:9;
    6833 = 5*1366 + 3; hence not 5 divides 6833 by NAT_4:9;
    6833 = 7*976 + 1; hence not 7 divides 6833 by NAT_4:9;
    6833 = 11*621 + 2; hence not 11 divides 6833 by NAT_4:9;
    6833 = 13*525 + 8; hence not 13 divides 6833 by NAT_4:9;
    6833 = 17*401 + 16; hence not 17 divides 6833 by NAT_4:9;
    6833 = 19*359 + 12; hence not 19 divides 6833 by NAT_4:9;
    6833 = 23*297 + 2; hence not 23 divides 6833 by NAT_4:9;
    6833 = 29*235 + 18; hence not 29 divides 6833 by NAT_4:9;
    6833 = 31*220 + 13; hence not 31 divides 6833 by NAT_4:9;
    6833 = 37*184 + 25; hence not 37 divides 6833 by NAT_4:9;
    6833 = 41*166 + 27; hence not 41 divides 6833 by NAT_4:9;
    6833 = 43*158 + 39; hence not 43 divides 6833 by NAT_4:9;
    6833 = 47*145 + 18; hence not 47 divides 6833 by NAT_4:9;
    6833 = 53*128 + 49; hence not 53 divides 6833 by NAT_4:9;
    6833 = 59*115 + 48; hence not 59 divides 6833 by NAT_4:9;
    6833 = 61*112 + 1; hence not 61 divides 6833 by NAT_4:9;
    6833 = 67*101 + 66; hence not 67 divides 6833 by NAT_4:9;
    6833 = 71*96 + 17; hence not 71 divides 6833 by NAT_4:9;
    6833 = 73*93 + 44; hence not 73 divides 6833 by NAT_4:9;
    6833 = 79*86 + 39; hence not 79 divides 6833 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6833 & n is prime
  holds not n divides 6833 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
