
theorem
  6007 is prime
proof
  now
    6007 = 2*3003 + 1; hence not 2 divides 6007 by NAT_4:9;
    6007 = 3*2002 + 1; hence not 3 divides 6007 by NAT_4:9;
    6007 = 5*1201 + 2; hence not 5 divides 6007 by NAT_4:9;
    6007 = 7*858 + 1; hence not 7 divides 6007 by NAT_4:9;
    6007 = 11*546 + 1; hence not 11 divides 6007 by NAT_4:9;
    6007 = 13*462 + 1; hence not 13 divides 6007 by NAT_4:9;
    6007 = 17*353 + 6; hence not 17 divides 6007 by NAT_4:9;
    6007 = 19*316 + 3; hence not 19 divides 6007 by NAT_4:9;
    6007 = 23*261 + 4; hence not 23 divides 6007 by NAT_4:9;
    6007 = 29*207 + 4; hence not 29 divides 6007 by NAT_4:9;
    6007 = 31*193 + 24; hence not 31 divides 6007 by NAT_4:9;
    6007 = 37*162 + 13; hence not 37 divides 6007 by NAT_4:9;
    6007 = 41*146 + 21; hence not 41 divides 6007 by NAT_4:9;
    6007 = 43*139 + 30; hence not 43 divides 6007 by NAT_4:9;
    6007 = 47*127 + 38; hence not 47 divides 6007 by NAT_4:9;
    6007 = 53*113 + 18; hence not 53 divides 6007 by NAT_4:9;
    6007 = 59*101 + 48; hence not 59 divides 6007 by NAT_4:9;
    6007 = 61*98 + 29; hence not 61 divides 6007 by NAT_4:9;
    6007 = 67*89 + 44; hence not 67 divides 6007 by NAT_4:9;
    6007 = 71*84 + 43; hence not 71 divides 6007 by NAT_4:9;
    6007 = 73*82 + 21; hence not 73 divides 6007 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6007 & n is prime
  holds not n divides 6007 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
