
theorem
  1621 is prime
proof
  now
    1621 = 2*810 + 1; hence not 2 divides 1621 by NAT_4:9;
    1621 = 3*540 + 1; hence not 3 divides 1621 by NAT_4:9;
    1621 = 5*324 + 1; hence not 5 divides 1621 by NAT_4:9;
    1621 = 7*231 + 4; hence not 7 divides 1621 by NAT_4:9;
    1621 = 11*147 + 4; hence not 11 divides 1621 by NAT_4:9;
    1621 = 13*124 + 9; hence not 13 divides 1621 by NAT_4:9;
    1621 = 17*95 + 6; hence not 17 divides 1621 by NAT_4:9;
    1621 = 19*85 + 6; hence not 19 divides 1621 by NAT_4:9;
    1621 = 23*70 + 11; hence not 23 divides 1621 by NAT_4:9;
    1621 = 29*55 + 26; hence not 29 divides 1621 by NAT_4:9;
    1621 = 31*52 + 9; hence not 31 divides 1621 by NAT_4:9;
    1621 = 37*43 + 30; hence not 37 divides 1621 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1621 & n is prime
  holds not n divides 1621 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
