
theorem
  1889 is prime
proof
  now
    1889 = 2*944 + 1; hence not 2 divides 1889 by NAT_4:9;
    1889 = 3*629 + 2; hence not 3 divides 1889 by NAT_4:9;
    1889 = 5*377 + 4; hence not 5 divides 1889 by NAT_4:9;
    1889 = 7*269 + 6; hence not 7 divides 1889 by NAT_4:9;
    1889 = 11*171 + 8; hence not 11 divides 1889 by NAT_4:9;
    1889 = 13*145 + 4; hence not 13 divides 1889 by NAT_4:9;
    1889 = 17*111 + 2; hence not 17 divides 1889 by NAT_4:9;
    1889 = 19*99 + 8; hence not 19 divides 1889 by NAT_4:9;
    1889 = 23*82 + 3; hence not 23 divides 1889 by NAT_4:9;
    1889 = 29*65 + 4; hence not 29 divides 1889 by NAT_4:9;
    1889 = 31*60 + 29; hence not 31 divides 1889 by NAT_4:9;
    1889 = 37*51 + 2; hence not 37 divides 1889 by NAT_4:9;
    1889 = 41*46 + 3; hence not 41 divides 1889 by NAT_4:9;
    1889 = 43*43 + 40; hence not 43 divides 1889 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1889 & n is prime
  holds not n divides 1889 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
