
theorem
  9007 is prime
proof
  now
    9007 = 2*4503 + 1; hence not 2 divides 9007 by NAT_4:9;
    9007 = 3*3002 + 1; hence not 3 divides 9007 by NAT_4:9;
    9007 = 5*1801 + 2; hence not 5 divides 9007 by NAT_4:9;
    9007 = 7*1286 + 5; hence not 7 divides 9007 by NAT_4:9;
    9007 = 11*818 + 9; hence not 11 divides 9007 by NAT_4:9;
    9007 = 13*692 + 11; hence not 13 divides 9007 by NAT_4:9;
    9007 = 17*529 + 14; hence not 17 divides 9007 by NAT_4:9;
    9007 = 19*474 + 1; hence not 19 divides 9007 by NAT_4:9;
    9007 = 23*391 + 14; hence not 23 divides 9007 by NAT_4:9;
    9007 = 29*310 + 17; hence not 29 divides 9007 by NAT_4:9;
    9007 = 31*290 + 17; hence not 31 divides 9007 by NAT_4:9;
    9007 = 37*243 + 16; hence not 37 divides 9007 by NAT_4:9;
    9007 = 41*219 + 28; hence not 41 divides 9007 by NAT_4:9;
    9007 = 43*209 + 20; hence not 43 divides 9007 by NAT_4:9;
    9007 = 47*191 + 30; hence not 47 divides 9007 by NAT_4:9;
    9007 = 53*169 + 50; hence not 53 divides 9007 by NAT_4:9;
    9007 = 59*152 + 39; hence not 59 divides 9007 by NAT_4:9;
    9007 = 61*147 + 40; hence not 61 divides 9007 by NAT_4:9;
    9007 = 67*134 + 29; hence not 67 divides 9007 by NAT_4:9;
    9007 = 71*126 + 61; hence not 71 divides 9007 by NAT_4:9;
    9007 = 73*123 + 28; hence not 73 divides 9007 by NAT_4:9;
    9007 = 79*114 + 1; hence not 79 divides 9007 by NAT_4:9;
    9007 = 83*108 + 43; hence not 83 divides 9007 by NAT_4:9;
    9007 = 89*101 + 18; hence not 89 divides 9007 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9007 & n is prime
  holds not n divides 9007 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
