
theorem
  6011 is prime
proof
  now
    6011 = 2*3005 + 1; hence not 2 divides 6011 by NAT_4:9;
    6011 = 3*2003 + 2; hence not 3 divides 6011 by NAT_4:9;
    6011 = 5*1202 + 1; hence not 5 divides 6011 by NAT_4:9;
    6011 = 7*858 + 5; hence not 7 divides 6011 by NAT_4:9;
    6011 = 11*546 + 5; hence not 11 divides 6011 by NAT_4:9;
    6011 = 13*462 + 5; hence not 13 divides 6011 by NAT_4:9;
    6011 = 17*353 + 10; hence not 17 divides 6011 by NAT_4:9;
    6011 = 19*316 + 7; hence not 19 divides 6011 by NAT_4:9;
    6011 = 23*261 + 8; hence not 23 divides 6011 by NAT_4:9;
    6011 = 29*207 + 8; hence not 29 divides 6011 by NAT_4:9;
    6011 = 31*193 + 28; hence not 31 divides 6011 by NAT_4:9;
    6011 = 37*162 + 17; hence not 37 divides 6011 by NAT_4:9;
    6011 = 41*146 + 25; hence not 41 divides 6011 by NAT_4:9;
    6011 = 43*139 + 34; hence not 43 divides 6011 by NAT_4:9;
    6011 = 47*127 + 42; hence not 47 divides 6011 by NAT_4:9;
    6011 = 53*113 + 22; hence not 53 divides 6011 by NAT_4:9;
    6011 = 59*101 + 52; hence not 59 divides 6011 by NAT_4:9;
    6011 = 61*98 + 33; hence not 61 divides 6011 by NAT_4:9;
    6011 = 67*89 + 48; hence not 67 divides 6011 by NAT_4:9;
    6011 = 71*84 + 47; hence not 71 divides 6011 by NAT_4:9;
    6011 = 73*82 + 25; hence not 73 divides 6011 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6011 & n is prime
  holds not n divides 6011 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
