
theorem
  6803 is prime
proof
  now
    6803 = 2*3401 + 1; hence not 2 divides 6803 by NAT_4:9;
    6803 = 3*2267 + 2; hence not 3 divides 6803 by NAT_4:9;
    6803 = 5*1360 + 3; hence not 5 divides 6803 by NAT_4:9;
    6803 = 7*971 + 6; hence not 7 divides 6803 by NAT_4:9;
    6803 = 11*618 + 5; hence not 11 divides 6803 by NAT_4:9;
    6803 = 13*523 + 4; hence not 13 divides 6803 by NAT_4:9;
    6803 = 17*400 + 3; hence not 17 divides 6803 by NAT_4:9;
    6803 = 19*358 + 1; hence not 19 divides 6803 by NAT_4:9;
    6803 = 23*295 + 18; hence not 23 divides 6803 by NAT_4:9;
    6803 = 29*234 + 17; hence not 29 divides 6803 by NAT_4:9;
    6803 = 31*219 + 14; hence not 31 divides 6803 by NAT_4:9;
    6803 = 37*183 + 32; hence not 37 divides 6803 by NAT_4:9;
    6803 = 41*165 + 38; hence not 41 divides 6803 by NAT_4:9;
    6803 = 43*158 + 9; hence not 43 divides 6803 by NAT_4:9;
    6803 = 47*144 + 35; hence not 47 divides 6803 by NAT_4:9;
    6803 = 53*128 + 19; hence not 53 divides 6803 by NAT_4:9;
    6803 = 59*115 + 18; hence not 59 divides 6803 by NAT_4:9;
    6803 = 61*111 + 32; hence not 61 divides 6803 by NAT_4:9;
    6803 = 67*101 + 36; hence not 67 divides 6803 by NAT_4:9;
    6803 = 71*95 + 58; hence not 71 divides 6803 by NAT_4:9;
    6803 = 73*93 + 14; hence not 73 divides 6803 by NAT_4:9;
    6803 = 79*86 + 9; hence not 79 divides 6803 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6803 & n is prime
  holds not n divides 6803 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
