
theorem
  929 is prime
proof
  now
    929 = 2*464 + 1; hence not 2 divides 929 by NAT_4:9;
    929 = 3*309 + 2; hence not 3 divides 929 by NAT_4:9;
    929 = 5*185 + 4; hence not 5 divides 929 by NAT_4:9;
    929 = 7*132 + 5; hence not 7 divides 929 by NAT_4:9;
    929 = 11*84 + 5; hence not 11 divides 929 by NAT_4:9;
    929 = 13*71 + 6; hence not 13 divides 929 by NAT_4:9;
    929 = 17*54 + 11; hence not 17 divides 929 by NAT_4:9;
    929 = 19*48 + 17; hence not 19 divides 929 by NAT_4:9;
    929 = 23*40 + 9; hence not 23 divides 929 by NAT_4:9;
    929 = 29*32 + 1; hence not 29 divides 929 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 929 & n is prime
  holds not n divides 929 by XPRIMET1:20;
  hence thesis by NAT_4:14;
