
theorem
  1619 is prime
proof
  now
    1619 = 2*809 + 1; hence not 2 divides 1619 by NAT_4:9;
    1619 = 3*539 + 2; hence not 3 divides 1619 by NAT_4:9;
    1619 = 5*323 + 4; hence not 5 divides 1619 by NAT_4:9;
    1619 = 7*231 + 2; hence not 7 divides 1619 by NAT_4:9;
    1619 = 11*147 + 2; hence not 11 divides 1619 by NAT_4:9;
    1619 = 13*124 + 7; hence not 13 divides 1619 by NAT_4:9;
    1619 = 17*95 + 4; hence not 17 divides 1619 by NAT_4:9;
    1619 = 19*85 + 4; hence not 19 divides 1619 by NAT_4:9;
    1619 = 23*70 + 9; hence not 23 divides 1619 by NAT_4:9;
    1619 = 29*55 + 24; hence not 29 divides 1619 by NAT_4:9;
    1619 = 31*52 + 7; hence not 31 divides 1619 by NAT_4:9;
    1619 = 37*43 + 28; hence not 37 divides 1619 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1619 & n is prime
  holds not n divides 1619 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
