
theorem
  2693 is prime
proof
  now
    2693 = 2*1346 + 1; hence not 2 divides 2693 by NAT_4:9;
    2693 = 3*897 + 2; hence not 3 divides 2693 by NAT_4:9;
    2693 = 5*538 + 3; hence not 5 divides 2693 by NAT_4:9;
    2693 = 7*384 + 5; hence not 7 divides 2693 by NAT_4:9;
    2693 = 11*244 + 9; hence not 11 divides 2693 by NAT_4:9;
    2693 = 13*207 + 2; hence not 13 divides 2693 by NAT_4:9;
    2693 = 17*158 + 7; hence not 17 divides 2693 by NAT_4:9;
    2693 = 19*141 + 14; hence not 19 divides 2693 by NAT_4:9;
    2693 = 23*117 + 2; hence not 23 divides 2693 by NAT_4:9;
    2693 = 29*92 + 25; hence not 29 divides 2693 by NAT_4:9;
    2693 = 31*86 + 27; hence not 31 divides 2693 by NAT_4:9;
    2693 = 37*72 + 29; hence not 37 divides 2693 by NAT_4:9;
    2693 = 41*65 + 28; hence not 41 divides 2693 by NAT_4:9;
    2693 = 43*62 + 27; hence not 43 divides 2693 by NAT_4:9;
    2693 = 47*57 + 14; hence not 47 divides 2693 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2693 & n is prime
  holds not n divides 2693 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
