
theorem
  2683 is prime
proof
  now
    2683 = 2*1341 + 1; hence not 2 divides 2683 by NAT_4:9;
    2683 = 3*894 + 1; hence not 3 divides 2683 by NAT_4:9;
    2683 = 5*536 + 3; hence not 5 divides 2683 by NAT_4:9;
    2683 = 7*383 + 2; hence not 7 divides 2683 by NAT_4:9;
    2683 = 11*243 + 10; hence not 11 divides 2683 by NAT_4:9;
    2683 = 13*206 + 5; hence not 13 divides 2683 by NAT_4:9;
    2683 = 17*157 + 14; hence not 17 divides 2683 by NAT_4:9;
    2683 = 19*141 + 4; hence not 19 divides 2683 by NAT_4:9;
    2683 = 23*116 + 15; hence not 23 divides 2683 by NAT_4:9;
    2683 = 29*92 + 15; hence not 29 divides 2683 by NAT_4:9;
    2683 = 31*86 + 17; hence not 31 divides 2683 by NAT_4:9;
    2683 = 37*72 + 19; hence not 37 divides 2683 by NAT_4:9;
    2683 = 41*65 + 18; hence not 41 divides 2683 by NAT_4:9;
    2683 = 43*62 + 17; hence not 43 divides 2683 by NAT_4:9;
    2683 = 47*57 + 4; hence not 47 divides 2683 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2683 & n is prime
  holds not n divides 2683 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
