
theorem
  1831 is prime
proof
  now
    1831 = 2*915 + 1; hence not 2 divides 1831 by NAT_4:9;
    1831 = 3*610 + 1; hence not 3 divides 1831 by NAT_4:9;
    1831 = 5*366 + 1; hence not 5 divides 1831 by NAT_4:9;
    1831 = 7*261 + 4; hence not 7 divides 1831 by NAT_4:9;
    1831 = 11*166 + 5; hence not 11 divides 1831 by NAT_4:9;
    1831 = 13*140 + 11; hence not 13 divides 1831 by NAT_4:9;
    1831 = 17*107 + 12; hence not 17 divides 1831 by NAT_4:9;
    1831 = 19*96 + 7; hence not 19 divides 1831 by NAT_4:9;
    1831 = 23*79 + 14; hence not 23 divides 1831 by NAT_4:9;
    1831 = 29*63 + 4; hence not 29 divides 1831 by NAT_4:9;
    1831 = 31*59 + 2; hence not 31 divides 1831 by NAT_4:9;
    1831 = 37*49 + 18; hence not 37 divides 1831 by NAT_4:9;
    1831 = 41*44 + 27; hence not 41 divides 1831 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1831 & n is prime
  holds not n divides 1831 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
