
theorem
  9001 is prime
proof
  now
    9001 = 2*4500 + 1; hence not 2 divides 9001 by NAT_4:9;
    9001 = 3*3000 + 1; hence not 3 divides 9001 by NAT_4:9;
    9001 = 5*1800 + 1; hence not 5 divides 9001 by NAT_4:9;
    9001 = 7*1285 + 6; hence not 7 divides 9001 by NAT_4:9;
    9001 = 11*818 + 3; hence not 11 divides 9001 by NAT_4:9;
    9001 = 13*692 + 5; hence not 13 divides 9001 by NAT_4:9;
    9001 = 17*529 + 8; hence not 17 divides 9001 by NAT_4:9;
    9001 = 19*473 + 14; hence not 19 divides 9001 by NAT_4:9;
    9001 = 23*391 + 8; hence not 23 divides 9001 by NAT_4:9;
    9001 = 29*310 + 11; hence not 29 divides 9001 by NAT_4:9;
    9001 = 31*290 + 11; hence not 31 divides 9001 by NAT_4:9;
    9001 = 37*243 + 10; hence not 37 divides 9001 by NAT_4:9;
    9001 = 41*219 + 22; hence not 41 divides 9001 by NAT_4:9;
    9001 = 43*209 + 14; hence not 43 divides 9001 by NAT_4:9;
    9001 = 47*191 + 24; hence not 47 divides 9001 by NAT_4:9;
    9001 = 53*169 + 44; hence not 53 divides 9001 by NAT_4:9;
    9001 = 59*152 + 33; hence not 59 divides 9001 by NAT_4:9;
    9001 = 61*147 + 34; hence not 61 divides 9001 by NAT_4:9;
    9001 = 67*134 + 23; hence not 67 divides 9001 by NAT_4:9;
    9001 = 71*126 + 55; hence not 71 divides 9001 by NAT_4:9;
    9001 = 73*123 + 22; hence not 73 divides 9001 by NAT_4:9;
    9001 = 79*113 + 74; hence not 79 divides 9001 by NAT_4:9;
    9001 = 83*108 + 37; hence not 83 divides 9001 by NAT_4:9;
    9001 = 89*101 + 12; hence not 89 divides 9001 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9001 & n is prime
  holds not n divides 9001 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
