
theorem
  9049 is prime
proof
  now
    9049 = 2*4524 + 1; hence not 2 divides 9049 by NAT_4:9;
    9049 = 3*3016 + 1; hence not 3 divides 9049 by NAT_4:9;
    9049 = 5*1809 + 4; hence not 5 divides 9049 by NAT_4:9;
    9049 = 7*1292 + 5; hence not 7 divides 9049 by NAT_4:9;
    9049 = 11*822 + 7; hence not 11 divides 9049 by NAT_4:9;
    9049 = 13*696 + 1; hence not 13 divides 9049 by NAT_4:9;
    9049 = 17*532 + 5; hence not 17 divides 9049 by NAT_4:9;
    9049 = 19*476 + 5; hence not 19 divides 9049 by NAT_4:9;
    9049 = 23*393 + 10; hence not 23 divides 9049 by NAT_4:9;
    9049 = 29*312 + 1; hence not 29 divides 9049 by NAT_4:9;
    9049 = 31*291 + 28; hence not 31 divides 9049 by NAT_4:9;
    9049 = 37*244 + 21; hence not 37 divides 9049 by NAT_4:9;
    9049 = 41*220 + 29; hence not 41 divides 9049 by NAT_4:9;
    9049 = 43*210 + 19; hence not 43 divides 9049 by NAT_4:9;
    9049 = 47*192 + 25; hence not 47 divides 9049 by NAT_4:9;
    9049 = 53*170 + 39; hence not 53 divides 9049 by NAT_4:9;
    9049 = 59*153 + 22; hence not 59 divides 9049 by NAT_4:9;
    9049 = 61*148 + 21; hence not 61 divides 9049 by NAT_4:9;
    9049 = 67*135 + 4; hence not 67 divides 9049 by NAT_4:9;
    9049 = 71*127 + 32; hence not 71 divides 9049 by NAT_4:9;
    9049 = 73*123 + 70; hence not 73 divides 9049 by NAT_4:9;
    9049 = 79*114 + 43; hence not 79 divides 9049 by NAT_4:9;
    9049 = 83*109 + 2; hence not 83 divides 9049 by NAT_4:9;
    9049 = 89*101 + 60; hence not 89 divides 9049 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9049 & n is prime
  holds not n divides 9049 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
