
theorem
  6763 is prime
proof
  now
    6763 = 2*3381 + 1; hence not 2 divides 6763 by NAT_4:9;
    6763 = 3*2254 + 1; hence not 3 divides 6763 by NAT_4:9;
    6763 = 5*1352 + 3; hence not 5 divides 6763 by NAT_4:9;
    6763 = 7*966 + 1; hence not 7 divides 6763 by NAT_4:9;
    6763 = 11*614 + 9; hence not 11 divides 6763 by NAT_4:9;
    6763 = 13*520 + 3; hence not 13 divides 6763 by NAT_4:9;
    6763 = 17*397 + 14; hence not 17 divides 6763 by NAT_4:9;
    6763 = 19*355 + 18; hence not 19 divides 6763 by NAT_4:9;
    6763 = 23*294 + 1; hence not 23 divides 6763 by NAT_4:9;
    6763 = 29*233 + 6; hence not 29 divides 6763 by NAT_4:9;
    6763 = 31*218 + 5; hence not 31 divides 6763 by NAT_4:9;
    6763 = 37*182 + 29; hence not 37 divides 6763 by NAT_4:9;
    6763 = 41*164 + 39; hence not 41 divides 6763 by NAT_4:9;
    6763 = 43*157 + 12; hence not 43 divides 6763 by NAT_4:9;
    6763 = 47*143 + 42; hence not 47 divides 6763 by NAT_4:9;
    6763 = 53*127 + 32; hence not 53 divides 6763 by NAT_4:9;
    6763 = 59*114 + 37; hence not 59 divides 6763 by NAT_4:9;
    6763 = 61*110 + 53; hence not 61 divides 6763 by NAT_4:9;
    6763 = 67*100 + 63; hence not 67 divides 6763 by NAT_4:9;
    6763 = 71*95 + 18; hence not 71 divides 6763 by NAT_4:9;
    6763 = 73*92 + 47; hence not 73 divides 6763 by NAT_4:9;
    6763 = 79*85 + 48; hence not 79 divides 6763 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6763 & n is prime
  holds not n divides 6763 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
