
theorem
  7393 is prime
proof
  now
    7393 = 2*3696 + 1; hence not 2 divides 7393 by NAT_4:9;
    7393 = 3*2464 + 1; hence not 3 divides 7393 by NAT_4:9;
    7393 = 5*1478 + 3; hence not 5 divides 7393 by NAT_4:9;
    7393 = 7*1056 + 1; hence not 7 divides 7393 by NAT_4:9;
    7393 = 11*672 + 1; hence not 11 divides 7393 by NAT_4:9;
    7393 = 13*568 + 9; hence not 13 divides 7393 by NAT_4:9;
    7393 = 17*434 + 15; hence not 17 divides 7393 by NAT_4:9;
    7393 = 19*389 + 2; hence not 19 divides 7393 by NAT_4:9;
    7393 = 23*321 + 10; hence not 23 divides 7393 by NAT_4:9;
    7393 = 29*254 + 27; hence not 29 divides 7393 by NAT_4:9;
    7393 = 31*238 + 15; hence not 31 divides 7393 by NAT_4:9;
    7393 = 37*199 + 30; hence not 37 divides 7393 by NAT_4:9;
    7393 = 41*180 + 13; hence not 41 divides 7393 by NAT_4:9;
    7393 = 43*171 + 40; hence not 43 divides 7393 by NAT_4:9;
    7393 = 47*157 + 14; hence not 47 divides 7393 by NAT_4:9;
    7393 = 53*139 + 26; hence not 53 divides 7393 by NAT_4:9;
    7393 = 59*125 + 18; hence not 59 divides 7393 by NAT_4:9;
    7393 = 61*121 + 12; hence not 61 divides 7393 by NAT_4:9;
    7393 = 67*110 + 23; hence not 67 divides 7393 by NAT_4:9;
    7393 = 71*104 + 9; hence not 71 divides 7393 by NAT_4:9;
    7393 = 73*101 + 20; hence not 73 divides 7393 by NAT_4:9;
    7393 = 79*93 + 46; hence not 79 divides 7393 by NAT_4:9;
    7393 = 83*89 + 6; hence not 83 divides 7393 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7393 & n is prime
  holds not n divides 7393 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
