
theorem
  1093 is prime
proof
  now
    1093 = 2*546 + 1; hence not 2 divides 1093 by NAT_4:9;
    1093 = 3*364 + 1; hence not 3 divides 1093 by NAT_4:9;
    1093 = 5*218 + 3; hence not 5 divides 1093 by NAT_4:9;
    1093 = 7*156 + 1; hence not 7 divides 1093 by NAT_4:9;
    1093 = 11*99 + 4; hence not 11 divides 1093 by NAT_4:9;
    1093 = 13*84 + 1; hence not 13 divides 1093 by NAT_4:9;
    1093 = 17*64 + 5; hence not 17 divides 1093 by NAT_4:9;
    1093 = 19*57 + 10; hence not 19 divides 1093 by NAT_4:9;
    1093 = 23*47 + 12; hence not 23 divides 1093 by NAT_4:9;
    1093 = 29*37 + 20; hence not 29 divides 1093 by NAT_4:9;
    1093 = 31*35 + 8; hence not 31 divides 1093 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1093 & n is prime
  holds not n divides 1093 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
