
theorem
  6113 is prime
proof
  now
    6113 = 2*3056 + 1; hence not 2 divides 6113 by NAT_4:9;
    6113 = 3*2037 + 2; hence not 3 divides 6113 by NAT_4:9;
    6113 = 5*1222 + 3; hence not 5 divides 6113 by NAT_4:9;
    6113 = 7*873 + 2; hence not 7 divides 6113 by NAT_4:9;
    6113 = 11*555 + 8; hence not 11 divides 6113 by NAT_4:9;
    6113 = 13*470 + 3; hence not 13 divides 6113 by NAT_4:9;
    6113 = 17*359 + 10; hence not 17 divides 6113 by NAT_4:9;
    6113 = 19*321 + 14; hence not 19 divides 6113 by NAT_4:9;
    6113 = 23*265 + 18; hence not 23 divides 6113 by NAT_4:9;
    6113 = 29*210 + 23; hence not 29 divides 6113 by NAT_4:9;
    6113 = 31*197 + 6; hence not 31 divides 6113 by NAT_4:9;
    6113 = 37*165 + 8; hence not 37 divides 6113 by NAT_4:9;
    6113 = 41*149 + 4; hence not 41 divides 6113 by NAT_4:9;
    6113 = 43*142 + 7; hence not 43 divides 6113 by NAT_4:9;
    6113 = 47*130 + 3; hence not 47 divides 6113 by NAT_4:9;
    6113 = 53*115 + 18; hence not 53 divides 6113 by NAT_4:9;
    6113 = 59*103 + 36; hence not 59 divides 6113 by NAT_4:9;
    6113 = 61*100 + 13; hence not 61 divides 6113 by NAT_4:9;
    6113 = 67*91 + 16; hence not 67 divides 6113 by NAT_4:9;
    6113 = 71*86 + 7; hence not 71 divides 6113 by NAT_4:9;
    6113 = 73*83 + 54; hence not 73 divides 6113 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6113 & n is prime
  holds not n divides 6113 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
