
theorem
  6793 is prime
proof
  now
    6793 = 2*3396 + 1; hence not 2 divides 6793 by NAT_4:9;
    6793 = 3*2264 + 1; hence not 3 divides 6793 by NAT_4:9;
    6793 = 5*1358 + 3; hence not 5 divides 6793 by NAT_4:9;
    6793 = 7*970 + 3; hence not 7 divides 6793 by NAT_4:9;
    6793 = 11*617 + 6; hence not 11 divides 6793 by NAT_4:9;
    6793 = 13*522 + 7; hence not 13 divides 6793 by NAT_4:9;
    6793 = 17*399 + 10; hence not 17 divides 6793 by NAT_4:9;
    6793 = 19*357 + 10; hence not 19 divides 6793 by NAT_4:9;
    6793 = 23*295 + 8; hence not 23 divides 6793 by NAT_4:9;
    6793 = 29*234 + 7; hence not 29 divides 6793 by NAT_4:9;
    6793 = 31*219 + 4; hence not 31 divides 6793 by NAT_4:9;
    6793 = 37*183 + 22; hence not 37 divides 6793 by NAT_4:9;
    6793 = 41*165 + 28; hence not 41 divides 6793 by NAT_4:9;
    6793 = 43*157 + 42; hence not 43 divides 6793 by NAT_4:9;
    6793 = 47*144 + 25; hence not 47 divides 6793 by NAT_4:9;
    6793 = 53*128 + 9; hence not 53 divides 6793 by NAT_4:9;
    6793 = 59*115 + 8; hence not 59 divides 6793 by NAT_4:9;
    6793 = 61*111 + 22; hence not 61 divides 6793 by NAT_4:9;
    6793 = 67*101 + 26; hence not 67 divides 6793 by NAT_4:9;
    6793 = 71*95 + 48; hence not 71 divides 6793 by NAT_4:9;
    6793 = 73*93 + 4; hence not 73 divides 6793 by NAT_4:9;
    6793 = 79*85 + 78; hence not 79 divides 6793 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6793 & n is prime
  holds not n divides 6793 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
