
theorem
  5591 is prime
proof
  now
    5591 = 2*2795 + 1; hence not 2 divides 5591 by NAT_4:9;
    5591 = 3*1863 + 2; hence not 3 divides 5591 by NAT_4:9;
    5591 = 5*1118 + 1; hence not 5 divides 5591 by NAT_4:9;
    5591 = 7*798 + 5; hence not 7 divides 5591 by NAT_4:9;
    5591 = 11*508 + 3; hence not 11 divides 5591 by NAT_4:9;
    5591 = 13*430 + 1; hence not 13 divides 5591 by NAT_4:9;
    5591 = 17*328 + 15; hence not 17 divides 5591 by NAT_4:9;
    5591 = 19*294 + 5; hence not 19 divides 5591 by NAT_4:9;
    5591 = 23*243 + 2; hence not 23 divides 5591 by NAT_4:9;
    5591 = 29*192 + 23; hence not 29 divides 5591 by NAT_4:9;
    5591 = 31*180 + 11; hence not 31 divides 5591 by NAT_4:9;
    5591 = 37*151 + 4; hence not 37 divides 5591 by NAT_4:9;
    5591 = 41*136 + 15; hence not 41 divides 5591 by NAT_4:9;
    5591 = 43*130 + 1; hence not 43 divides 5591 by NAT_4:9;
    5591 = 47*118 + 45; hence not 47 divides 5591 by NAT_4:9;
    5591 = 53*105 + 26; hence not 53 divides 5591 by NAT_4:9;
    5591 = 59*94 + 45; hence not 59 divides 5591 by NAT_4:9;
    5591 = 61*91 + 40; hence not 61 divides 5591 by NAT_4:9;
    5591 = 67*83 + 30; hence not 67 divides 5591 by NAT_4:9;
    5591 = 71*78 + 53; hence not 71 divides 5591 by NAT_4:9;
    5591 = 73*76 + 43; hence not 73 divides 5591 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5591 & n is prime
  holds not n divides 5591 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
