
theorem
  9029 is prime
proof
  now
    9029 = 2*4514 + 1; hence not 2 divides 9029 by NAT_4:9;
    9029 = 3*3009 + 2; hence not 3 divides 9029 by NAT_4:9;
    9029 = 5*1805 + 4; hence not 5 divides 9029 by NAT_4:9;
    9029 = 7*1289 + 6; hence not 7 divides 9029 by NAT_4:9;
    9029 = 11*820 + 9; hence not 11 divides 9029 by NAT_4:9;
    9029 = 13*694 + 7; hence not 13 divides 9029 by NAT_4:9;
    9029 = 17*531 + 2; hence not 17 divides 9029 by NAT_4:9;
    9029 = 19*475 + 4; hence not 19 divides 9029 by NAT_4:9;
    9029 = 23*392 + 13; hence not 23 divides 9029 by NAT_4:9;
    9029 = 29*311 + 10; hence not 29 divides 9029 by NAT_4:9;
    9029 = 31*291 + 8; hence not 31 divides 9029 by NAT_4:9;
    9029 = 37*244 + 1; hence not 37 divides 9029 by NAT_4:9;
    9029 = 41*220 + 9; hence not 41 divides 9029 by NAT_4:9;
    9029 = 43*209 + 42; hence not 43 divides 9029 by NAT_4:9;
    9029 = 47*192 + 5; hence not 47 divides 9029 by NAT_4:9;
    9029 = 53*170 + 19; hence not 53 divides 9029 by NAT_4:9;
    9029 = 59*153 + 2; hence not 59 divides 9029 by NAT_4:9;
    9029 = 61*148 + 1; hence not 61 divides 9029 by NAT_4:9;
    9029 = 67*134 + 51; hence not 67 divides 9029 by NAT_4:9;
    9029 = 71*127 + 12; hence not 71 divides 9029 by NAT_4:9;
    9029 = 73*123 + 50; hence not 73 divides 9029 by NAT_4:9;
    9029 = 79*114 + 23; hence not 79 divides 9029 by NAT_4:9;
    9029 = 83*108 + 65; hence not 83 divides 9029 by NAT_4:9;
    9029 = 89*101 + 40; hence not 89 divides 9029 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9029 & n is prime
  holds not n divides 9029 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
