
theorem
  1427 is prime
proof
  now
    1427 = 2*713 + 1; hence not 2 divides 1427 by NAT_4:9;
    1427 = 3*475 + 2; hence not 3 divides 1427 by NAT_4:9;
    1427 = 5*285 + 2; hence not 5 divides 1427 by NAT_4:9;
    1427 = 7*203 + 6; hence not 7 divides 1427 by NAT_4:9;
    1427 = 11*129 + 8; hence not 11 divides 1427 by NAT_4:9;
    1427 = 13*109 + 10; hence not 13 divides 1427 by NAT_4:9;
    1427 = 17*83 + 16; hence not 17 divides 1427 by NAT_4:9;
    1427 = 19*75 + 2; hence not 19 divides 1427 by NAT_4:9;
    1427 = 23*62 + 1; hence not 23 divides 1427 by NAT_4:9;
    1427 = 29*49 + 6; hence not 29 divides 1427 by NAT_4:9;
    1427 = 31*46 + 1; hence not 31 divides 1427 by NAT_4:9;
    1427 = 37*38 + 21; hence not 37 divides 1427 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1427 & n is prime
  holds not n divides 1427 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
