
theorem
  6779 is prime
proof
  now
    6779 = 2*3389 + 1; hence not 2 divides 6779 by NAT_4:9;
    6779 = 3*2259 + 2; hence not 3 divides 6779 by NAT_4:9;
    6779 = 5*1355 + 4; hence not 5 divides 6779 by NAT_4:9;
    6779 = 7*968 + 3; hence not 7 divides 6779 by NAT_4:9;
    6779 = 11*616 + 3; hence not 11 divides 6779 by NAT_4:9;
    6779 = 13*521 + 6; hence not 13 divides 6779 by NAT_4:9;
    6779 = 17*398 + 13; hence not 17 divides 6779 by NAT_4:9;
    6779 = 19*356 + 15; hence not 19 divides 6779 by NAT_4:9;
    6779 = 23*294 + 17; hence not 23 divides 6779 by NAT_4:9;
    6779 = 29*233 + 22; hence not 29 divides 6779 by NAT_4:9;
    6779 = 31*218 + 21; hence not 31 divides 6779 by NAT_4:9;
    6779 = 37*183 + 8; hence not 37 divides 6779 by NAT_4:9;
    6779 = 41*165 + 14; hence not 41 divides 6779 by NAT_4:9;
    6779 = 43*157 + 28; hence not 43 divides 6779 by NAT_4:9;
    6779 = 47*144 + 11; hence not 47 divides 6779 by NAT_4:9;
    6779 = 53*127 + 48; hence not 53 divides 6779 by NAT_4:9;
    6779 = 59*114 + 53; hence not 59 divides 6779 by NAT_4:9;
    6779 = 61*111 + 8; hence not 61 divides 6779 by NAT_4:9;
    6779 = 67*101 + 12; hence not 67 divides 6779 by NAT_4:9;
    6779 = 71*95 + 34; hence not 71 divides 6779 by NAT_4:9;
    6779 = 73*92 + 63; hence not 73 divides 6779 by NAT_4:9;
    6779 = 79*85 + 64; hence not 79 divides 6779 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6779 & n is prime
  holds not n divides 6779 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
