
theorem
  7243 is prime
proof
  now
    7243 = 2*3621 + 1; hence not 2 divides 7243 by NAT_4:9;
    7243 = 3*2414 + 1; hence not 3 divides 7243 by NAT_4:9;
    7243 = 5*1448 + 3; hence not 5 divides 7243 by NAT_4:9;
    7243 = 7*1034 + 5; hence not 7 divides 7243 by NAT_4:9;
    7243 = 11*658 + 5; hence not 11 divides 7243 by NAT_4:9;
    7243 = 13*557 + 2; hence not 13 divides 7243 by NAT_4:9;
    7243 = 17*426 + 1; hence not 17 divides 7243 by NAT_4:9;
    7243 = 19*381 + 4; hence not 19 divides 7243 by NAT_4:9;
    7243 = 23*314 + 21; hence not 23 divides 7243 by NAT_4:9;
    7243 = 29*249 + 22; hence not 29 divides 7243 by NAT_4:9;
    7243 = 31*233 + 20; hence not 31 divides 7243 by NAT_4:9;
    7243 = 37*195 + 28; hence not 37 divides 7243 by NAT_4:9;
    7243 = 41*176 + 27; hence not 41 divides 7243 by NAT_4:9;
    7243 = 43*168 + 19; hence not 43 divides 7243 by NAT_4:9;
    7243 = 47*154 + 5; hence not 47 divides 7243 by NAT_4:9;
    7243 = 53*136 + 35; hence not 53 divides 7243 by NAT_4:9;
    7243 = 59*122 + 45; hence not 59 divides 7243 by NAT_4:9;
    7243 = 61*118 + 45; hence not 61 divides 7243 by NAT_4:9;
    7243 = 67*108 + 7; hence not 67 divides 7243 by NAT_4:9;
    7243 = 71*102 + 1; hence not 71 divides 7243 by NAT_4:9;
    7243 = 73*99 + 16; hence not 73 divides 7243 by NAT_4:9;
    7243 = 79*91 + 54; hence not 79 divides 7243 by NAT_4:9;
    7243 = 83*87 + 22; hence not 83 divides 7243 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7243 & n is prime
  holds not n divides 7243 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
