
theorem
  2621 is prime
proof
  now
    2621 = 2*1310 + 1; hence not 2 divides 2621 by NAT_4:9;
    2621 = 3*873 + 2; hence not 3 divides 2621 by NAT_4:9;
    2621 = 5*524 + 1; hence not 5 divides 2621 by NAT_4:9;
    2621 = 7*374 + 3; hence not 7 divides 2621 by NAT_4:9;
    2621 = 11*238 + 3; hence not 11 divides 2621 by NAT_4:9;
    2621 = 13*201 + 8; hence not 13 divides 2621 by NAT_4:9;
    2621 = 17*154 + 3; hence not 17 divides 2621 by NAT_4:9;
    2621 = 19*137 + 18; hence not 19 divides 2621 by NAT_4:9;
    2621 = 23*113 + 22; hence not 23 divides 2621 by NAT_4:9;
    2621 = 29*90 + 11; hence not 29 divides 2621 by NAT_4:9;
    2621 = 31*84 + 17; hence not 31 divides 2621 by NAT_4:9;
    2621 = 37*70 + 31; hence not 37 divides 2621 by NAT_4:9;
    2621 = 41*63 + 38; hence not 41 divides 2621 by NAT_4:9;
    2621 = 43*60 + 41; hence not 43 divides 2621 by NAT_4:9;
    2621 = 47*55 + 36; hence not 47 divides 2621 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2621 & n is prime
  holds not n divides 2621 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
