
theorem
  6091 is prime
proof
  now
    6091 = 2*3045 + 1; hence not 2 divides 6091 by NAT_4:9;
    6091 = 3*2030 + 1; hence not 3 divides 6091 by NAT_4:9;
    6091 = 5*1218 + 1; hence not 5 divides 6091 by NAT_4:9;
    6091 = 7*870 + 1; hence not 7 divides 6091 by NAT_4:9;
    6091 = 11*553 + 8; hence not 11 divides 6091 by NAT_4:9;
    6091 = 13*468 + 7; hence not 13 divides 6091 by NAT_4:9;
    6091 = 17*358 + 5; hence not 17 divides 6091 by NAT_4:9;
    6091 = 19*320 + 11; hence not 19 divides 6091 by NAT_4:9;
    6091 = 23*264 + 19; hence not 23 divides 6091 by NAT_4:9;
    6091 = 29*210 + 1; hence not 29 divides 6091 by NAT_4:9;
    6091 = 31*196 + 15; hence not 31 divides 6091 by NAT_4:9;
    6091 = 37*164 + 23; hence not 37 divides 6091 by NAT_4:9;
    6091 = 41*148 + 23; hence not 41 divides 6091 by NAT_4:9;
    6091 = 43*141 + 28; hence not 43 divides 6091 by NAT_4:9;
    6091 = 47*129 + 28; hence not 47 divides 6091 by NAT_4:9;
    6091 = 53*114 + 49; hence not 53 divides 6091 by NAT_4:9;
    6091 = 59*103 + 14; hence not 59 divides 6091 by NAT_4:9;
    6091 = 61*99 + 52; hence not 61 divides 6091 by NAT_4:9;
    6091 = 67*90 + 61; hence not 67 divides 6091 by NAT_4:9;
    6091 = 71*85 + 56; hence not 71 divides 6091 by NAT_4:9;
    6091 = 73*83 + 32; hence not 73 divides 6091 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6091 & n is prime
  holds not n divides 6091 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
