
theorem
  7573 is prime
proof
  now
    7573 = 2*3786 + 1; hence not 2 divides 7573 by NAT_4:9;
    7573 = 3*2524 + 1; hence not 3 divides 7573 by NAT_4:9;
    7573 = 5*1514 + 3; hence not 5 divides 7573 by NAT_4:9;
    7573 = 7*1081 + 6; hence not 7 divides 7573 by NAT_4:9;
    7573 = 11*688 + 5; hence not 11 divides 7573 by NAT_4:9;
    7573 = 13*582 + 7; hence not 13 divides 7573 by NAT_4:9;
    7573 = 17*445 + 8; hence not 17 divides 7573 by NAT_4:9;
    7573 = 19*398 + 11; hence not 19 divides 7573 by NAT_4:9;
    7573 = 23*329 + 6; hence not 23 divides 7573 by NAT_4:9;
    7573 = 29*261 + 4; hence not 29 divides 7573 by NAT_4:9;
    7573 = 31*244 + 9; hence not 31 divides 7573 by NAT_4:9;
    7573 = 37*204 + 25; hence not 37 divides 7573 by NAT_4:9;
    7573 = 41*184 + 29; hence not 41 divides 7573 by NAT_4:9;
    7573 = 43*176 + 5; hence not 43 divides 7573 by NAT_4:9;
    7573 = 47*161 + 6; hence not 47 divides 7573 by NAT_4:9;
    7573 = 53*142 + 47; hence not 53 divides 7573 by NAT_4:9;
    7573 = 59*128 + 21; hence not 59 divides 7573 by NAT_4:9;
    7573 = 61*124 + 9; hence not 61 divides 7573 by NAT_4:9;
    7573 = 67*113 + 2; hence not 67 divides 7573 by NAT_4:9;
    7573 = 71*106 + 47; hence not 71 divides 7573 by NAT_4:9;
    7573 = 73*103 + 54; hence not 73 divides 7573 by NAT_4:9;
    7573 = 79*95 + 68; hence not 79 divides 7573 by NAT_4:9;
    7573 = 83*91 + 20; hence not 83 divides 7573 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7573 & n is prime
  holds not n divides 7573 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
