
theorem
  1231 is prime
proof
  now
    1231 = 2*615 + 1; hence not 2 divides 1231 by NAT_4:9;
    1231 = 3*410 + 1; hence not 3 divides 1231 by NAT_4:9;
    1231 = 5*246 + 1; hence not 5 divides 1231 by NAT_4:9;
    1231 = 7*175 + 6; hence not 7 divides 1231 by NAT_4:9;
    1231 = 11*111 + 10; hence not 11 divides 1231 by NAT_4:9;
    1231 = 13*94 + 9; hence not 13 divides 1231 by NAT_4:9;
    1231 = 17*72 + 7; hence not 17 divides 1231 by NAT_4:9;
    1231 = 19*64 + 15; hence not 19 divides 1231 by NAT_4:9;
    1231 = 23*53 + 12; hence not 23 divides 1231 by NAT_4:9;
    1231 = 29*42 + 13; hence not 29 divides 1231 by NAT_4:9;
    1231 = 31*39 + 22; hence not 31 divides 1231 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1231 & n is prime
  holds not n divides 1231 by XPRIMET1:22;
  hence thesis by NAT_4:14;
