
theorem
  4391 is prime
proof
  now
    4391 = 2*2195 + 1; hence not 2 divides 4391 by NAT_4:9;
    4391 = 3*1463 + 2; hence not 3 divides 4391 by NAT_4:9;
    4391 = 5*878 + 1; hence not 5 divides 4391 by NAT_4:9;
    4391 = 7*627 + 2; hence not 7 divides 4391 by NAT_4:9;
    4391 = 11*399 + 2; hence not 11 divides 4391 by NAT_4:9;
    4391 = 13*337 + 10; hence not 13 divides 4391 by NAT_4:9;
    4391 = 17*258 + 5; hence not 17 divides 4391 by NAT_4:9;
    4391 = 19*231 + 2; hence not 19 divides 4391 by NAT_4:9;
    4391 = 23*190 + 21; hence not 23 divides 4391 by NAT_4:9;
    4391 = 29*151 + 12; hence not 29 divides 4391 by NAT_4:9;
    4391 = 31*141 + 20; hence not 31 divides 4391 by NAT_4:9;
    4391 = 37*118 + 25; hence not 37 divides 4391 by NAT_4:9;
    4391 = 41*107 + 4; hence not 41 divides 4391 by NAT_4:9;
    4391 = 43*102 + 5; hence not 43 divides 4391 by NAT_4:9;
    4391 = 47*93 + 20; hence not 47 divides 4391 by NAT_4:9;
    4391 = 53*82 + 45; hence not 53 divides 4391 by NAT_4:9;
    4391 = 59*74 + 25; hence not 59 divides 4391 by NAT_4:9;
    4391 = 61*71 + 60; hence not 61 divides 4391 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4391 & n is prime
  holds not n divides 4391 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
