
theorem
  1061 is prime
proof
  now
    1061 = 2*530 + 1; hence not 2 divides 1061 by NAT_4:9;
    1061 = 3*353 + 2; hence not 3 divides 1061 by NAT_4:9;
    1061 = 5*212 + 1; hence not 5 divides 1061 by NAT_4:9;
    1061 = 7*151 + 4; hence not 7 divides 1061 by NAT_4:9;
    1061 = 11*96 + 5; hence not 11 divides 1061 by NAT_4:9;
    1061 = 13*81 + 8; hence not 13 divides 1061 by NAT_4:9;
    1061 = 17*62 + 7; hence not 17 divides 1061 by NAT_4:9;
    1061 = 19*55 + 16; hence not 19 divides 1061 by NAT_4:9;
    1061 = 23*46 + 3; hence not 23 divides 1061 by NAT_4:9;
    1061 = 29*36 + 17; hence not 29 divides 1061 by NAT_4:9;
    1061 = 31*34 + 7; hence not 31 divides 1061 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1061 & n is prime
  holds not n divides 1061 by XPRIMET1:22;
  hence thesis by NAT_4:14;
