
theorem
  6301 is prime
proof
  now
    6301 = 2*3150 + 1; hence not 2 divides 6301 by NAT_4:9;
    6301 = 3*2100 + 1; hence not 3 divides 6301 by NAT_4:9;
    6301 = 5*1260 + 1; hence not 5 divides 6301 by NAT_4:9;
    6301 = 7*900 + 1; hence not 7 divides 6301 by NAT_4:9;
    6301 = 11*572 + 9; hence not 11 divides 6301 by NAT_4:9;
    6301 = 13*484 + 9; hence not 13 divides 6301 by NAT_4:9;
    6301 = 17*370 + 11; hence not 17 divides 6301 by NAT_4:9;
    6301 = 19*331 + 12; hence not 19 divides 6301 by NAT_4:9;
    6301 = 23*273 + 22; hence not 23 divides 6301 by NAT_4:9;
    6301 = 29*217 + 8; hence not 29 divides 6301 by NAT_4:9;
    6301 = 31*203 + 8; hence not 31 divides 6301 by NAT_4:9;
    6301 = 37*170 + 11; hence not 37 divides 6301 by NAT_4:9;
    6301 = 41*153 + 28; hence not 41 divides 6301 by NAT_4:9;
    6301 = 43*146 + 23; hence not 43 divides 6301 by NAT_4:9;
    6301 = 47*134 + 3; hence not 47 divides 6301 by NAT_4:9;
    6301 = 53*118 + 47; hence not 53 divides 6301 by NAT_4:9;
    6301 = 59*106 + 47; hence not 59 divides 6301 by NAT_4:9;
    6301 = 61*103 + 18; hence not 61 divides 6301 by NAT_4:9;
    6301 = 67*94 + 3; hence not 67 divides 6301 by NAT_4:9;
    6301 = 71*88 + 53; hence not 71 divides 6301 by NAT_4:9;
    6301 = 73*86 + 23; hence not 73 divides 6301 by NAT_4:9;
    6301 = 79*79 + 60; hence not 79 divides 6301 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6301 & n is prime
  holds not n divides 6301 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
