
theorem
  7193 is prime
proof
  now
    7193 = 2*3596 + 1; hence not 2 divides 7193 by NAT_4:9;
    7193 = 3*2397 + 2; hence not 3 divides 7193 by NAT_4:9;
    7193 = 5*1438 + 3; hence not 5 divides 7193 by NAT_4:9;
    7193 = 7*1027 + 4; hence not 7 divides 7193 by NAT_4:9;
    7193 = 11*653 + 10; hence not 11 divides 7193 by NAT_4:9;
    7193 = 13*553 + 4; hence not 13 divides 7193 by NAT_4:9;
    7193 = 17*423 + 2; hence not 17 divides 7193 by NAT_4:9;
    7193 = 19*378 + 11; hence not 19 divides 7193 by NAT_4:9;
    7193 = 23*312 + 17; hence not 23 divides 7193 by NAT_4:9;
    7193 = 29*248 + 1; hence not 29 divides 7193 by NAT_4:9;
    7193 = 31*232 + 1; hence not 31 divides 7193 by NAT_4:9;
    7193 = 37*194 + 15; hence not 37 divides 7193 by NAT_4:9;
    7193 = 41*175 + 18; hence not 41 divides 7193 by NAT_4:9;
    7193 = 43*167 + 12; hence not 43 divides 7193 by NAT_4:9;
    7193 = 47*153 + 2; hence not 47 divides 7193 by NAT_4:9;
    7193 = 53*135 + 38; hence not 53 divides 7193 by NAT_4:9;
    7193 = 59*121 + 54; hence not 59 divides 7193 by NAT_4:9;
    7193 = 61*117 + 56; hence not 61 divides 7193 by NAT_4:9;
    7193 = 67*107 + 24; hence not 67 divides 7193 by NAT_4:9;
    7193 = 71*101 + 22; hence not 71 divides 7193 by NAT_4:9;
    7193 = 73*98 + 39; hence not 73 divides 7193 by NAT_4:9;
    7193 = 79*91 + 4; hence not 79 divides 7193 by NAT_4:9;
    7193 = 83*86 + 55; hence not 83 divides 7193 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7193 & n is prime
  holds not n divides 7193 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
