
theorem
  1069 is prime
proof
  now
    1069 = 2*534 + 1; hence not 2 divides 1069 by NAT_4:9;
    1069 = 3*356 + 1; hence not 3 divides 1069 by NAT_4:9;
    1069 = 5*213 + 4; hence not 5 divides 1069 by NAT_4:9;
    1069 = 7*152 + 5; hence not 7 divides 1069 by NAT_4:9;
    1069 = 11*97 + 2; hence not 11 divides 1069 by NAT_4:9;
    1069 = 13*82 + 3; hence not 13 divides 1069 by NAT_4:9;
    1069 = 17*62 + 15; hence not 17 divides 1069 by NAT_4:9;
    1069 = 19*56 + 5; hence not 19 divides 1069 by NAT_4:9;
    1069 = 23*46 + 11; hence not 23 divides 1069 by NAT_4:9;
    1069 = 29*36 + 25; hence not 29 divides 1069 by NAT_4:9;
    1069 = 31*34 + 15; hence not 31 divides 1069 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1069 & n is prime
  holds not n divides 1069 by XPRIMET1:22;
  hence thesis by NAT_4:14;
