
theorem
  1063 is prime
proof
  now
    1063 = 2*531 + 1; hence not 2 divides 1063 by NAT_4:9;
    1063 = 3*354 + 1; hence not 3 divides 1063 by NAT_4:9;
    1063 = 5*212 + 3; hence not 5 divides 1063 by NAT_4:9;
    1063 = 7*151 + 6; hence not 7 divides 1063 by NAT_4:9;
    1063 = 11*96 + 7; hence not 11 divides 1063 by NAT_4:9;
    1063 = 13*81 + 10; hence not 13 divides 1063 by NAT_4:9;
    1063 = 17*62 + 9; hence not 17 divides 1063 by NAT_4:9;
    1063 = 19*55 + 18; hence not 19 divides 1063 by NAT_4:9;
    1063 = 23*46 + 5; hence not 23 divides 1063 by NAT_4:9;
    1063 = 29*36 + 19; hence not 29 divides 1063 by NAT_4:9;
    1063 = 31*34 + 9; hence not 31 divides 1063 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1063 & n is prime
  holds not n divides 1063 by XPRIMET1:22;
  hence thesis by NAT_4:14;
