
theorem
  7603 is prime
proof
  now
    7603 = 2*3801 + 1; hence not 2 divides 7603 by NAT_4:9;
    7603 = 3*2534 + 1; hence not 3 divides 7603 by NAT_4:9;
    7603 = 5*1520 + 3; hence not 5 divides 7603 by NAT_4:9;
    7603 = 7*1086 + 1; hence not 7 divides 7603 by NAT_4:9;
    7603 = 11*691 + 2; hence not 11 divides 7603 by NAT_4:9;
    7603 = 13*584 + 11; hence not 13 divides 7603 by NAT_4:9;
    7603 = 17*447 + 4; hence not 17 divides 7603 by NAT_4:9;
    7603 = 19*400 + 3; hence not 19 divides 7603 by NAT_4:9;
    7603 = 23*330 + 13; hence not 23 divides 7603 by NAT_4:9;
    7603 = 29*262 + 5; hence not 29 divides 7603 by NAT_4:9;
    7603 = 31*245 + 8; hence not 31 divides 7603 by NAT_4:9;
    7603 = 37*205 + 18; hence not 37 divides 7603 by NAT_4:9;
    7603 = 41*185 + 18; hence not 41 divides 7603 by NAT_4:9;
    7603 = 43*176 + 35; hence not 43 divides 7603 by NAT_4:9;
    7603 = 47*161 + 36; hence not 47 divides 7603 by NAT_4:9;
    7603 = 53*143 + 24; hence not 53 divides 7603 by NAT_4:9;
    7603 = 59*128 + 51; hence not 59 divides 7603 by NAT_4:9;
    7603 = 61*124 + 39; hence not 61 divides 7603 by NAT_4:9;
    7603 = 67*113 + 32; hence not 67 divides 7603 by NAT_4:9;
    7603 = 71*107 + 6; hence not 71 divides 7603 by NAT_4:9;
    7603 = 73*104 + 11; hence not 73 divides 7603 by NAT_4:9;
    7603 = 79*96 + 19; hence not 79 divides 7603 by NAT_4:9;
    7603 = 83*91 + 50; hence not 83 divides 7603 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7603 & n is prime
  holds not n divides 7603 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
