
theorem
  1031 is prime
proof
  now
    1031 = 2*515 + 1; hence not 2 divides 1031 by NAT_4:9;
    1031 = 3*343 + 2; hence not 3 divides 1031 by NAT_4:9;
    1031 = 5*206 + 1; hence not 5 divides 1031 by NAT_4:9;
    1031 = 7*147 + 2; hence not 7 divides 1031 by NAT_4:9;
    1031 = 11*93 + 8; hence not 11 divides 1031 by NAT_4:9;
    1031 = 13*79 + 4; hence not 13 divides 1031 by NAT_4:9;
    1031 = 17*60 + 11; hence not 17 divides 1031 by NAT_4:9;
    1031 = 19*54 + 5; hence not 19 divides 1031 by NAT_4:9;
    1031 = 23*44 + 19; hence not 23 divides 1031 by NAT_4:9;
    1031 = 29*35 + 16; hence not 29 divides 1031 by NAT_4:9;
    1031 = 31*33 + 8; hence not 31 divides 1031 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1031 & n is prime
  holds not n divides 1031 by XPRIMET1:22;
  hence thesis by NAT_4:14;
