
theorem
  7489 is prime
proof
  now
    7489 = 2*3744 + 1; hence not 2 divides 7489 by NAT_4:9;
    7489 = 3*2496 + 1; hence not 3 divides 7489 by NAT_4:9;
    7489 = 5*1497 + 4; hence not 5 divides 7489 by NAT_4:9;
    7489 = 7*1069 + 6; hence not 7 divides 7489 by NAT_4:9;
    7489 = 11*680 + 9; hence not 11 divides 7489 by NAT_4:9;
    7489 = 13*576 + 1; hence not 13 divides 7489 by NAT_4:9;
    7489 = 17*440 + 9; hence not 17 divides 7489 by NAT_4:9;
    7489 = 19*394 + 3; hence not 19 divides 7489 by NAT_4:9;
    7489 = 23*325 + 14; hence not 23 divides 7489 by NAT_4:9;
    7489 = 29*258 + 7; hence not 29 divides 7489 by NAT_4:9;
    7489 = 31*241 + 18; hence not 31 divides 7489 by NAT_4:9;
    7489 = 37*202 + 15; hence not 37 divides 7489 by NAT_4:9;
    7489 = 41*182 + 27; hence not 41 divides 7489 by NAT_4:9;
    7489 = 43*174 + 7; hence not 43 divides 7489 by NAT_4:9;
    7489 = 47*159 + 16; hence not 47 divides 7489 by NAT_4:9;
    7489 = 53*141 + 16; hence not 53 divides 7489 by NAT_4:9;
    7489 = 59*126 + 55; hence not 59 divides 7489 by NAT_4:9;
    7489 = 61*122 + 47; hence not 61 divides 7489 by NAT_4:9;
    7489 = 67*111 + 52; hence not 67 divides 7489 by NAT_4:9;
    7489 = 71*105 + 34; hence not 71 divides 7489 by NAT_4:9;
    7489 = 73*102 + 43; hence not 73 divides 7489 by NAT_4:9;
    7489 = 79*94 + 63; hence not 79 divides 7489 by NAT_4:9;
    7489 = 83*90 + 19; hence not 83 divides 7489 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7489 & n is prime
  holds not n divides 7489 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
