
theorem
  6791 is prime
proof
  now
    6791 = 2*3395 + 1; hence not 2 divides 6791 by NAT_4:9;
    6791 = 3*2263 + 2; hence not 3 divides 6791 by NAT_4:9;
    6791 = 5*1358 + 1; hence not 5 divides 6791 by NAT_4:9;
    6791 = 7*970 + 1; hence not 7 divides 6791 by NAT_4:9;
    6791 = 11*617 + 4; hence not 11 divides 6791 by NAT_4:9;
    6791 = 13*522 + 5; hence not 13 divides 6791 by NAT_4:9;
    6791 = 17*399 + 8; hence not 17 divides 6791 by NAT_4:9;
    6791 = 19*357 + 8; hence not 19 divides 6791 by NAT_4:9;
    6791 = 23*295 + 6; hence not 23 divides 6791 by NAT_4:9;
    6791 = 29*234 + 5; hence not 29 divides 6791 by NAT_4:9;
    6791 = 31*219 + 2; hence not 31 divides 6791 by NAT_4:9;
    6791 = 37*183 + 20; hence not 37 divides 6791 by NAT_4:9;
    6791 = 41*165 + 26; hence not 41 divides 6791 by NAT_4:9;
    6791 = 43*157 + 40; hence not 43 divides 6791 by NAT_4:9;
    6791 = 47*144 + 23; hence not 47 divides 6791 by NAT_4:9;
    6791 = 53*128 + 7; hence not 53 divides 6791 by NAT_4:9;
    6791 = 59*115 + 6; hence not 59 divides 6791 by NAT_4:9;
    6791 = 61*111 + 20; hence not 61 divides 6791 by NAT_4:9;
    6791 = 67*101 + 24; hence not 67 divides 6791 by NAT_4:9;
    6791 = 71*95 + 46; hence not 71 divides 6791 by NAT_4:9;
    6791 = 73*93 + 2; hence not 73 divides 6791 by NAT_4:9;
    6791 = 79*85 + 76; hence not 79 divides 6791 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6791 & n is prime
  holds not n divides 6791 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
