
theorem
  1217 is prime
proof
  now
    1217 = 2*608 + 1; hence not 2 divides 1217 by NAT_4:9;
    1217 = 3*405 + 2; hence not 3 divides 1217 by NAT_4:9;
    1217 = 5*243 + 2; hence not 5 divides 1217 by NAT_4:9;
    1217 = 7*173 + 6; hence not 7 divides 1217 by NAT_4:9;
    1217 = 11*110 + 7; hence not 11 divides 1217 by NAT_4:9;
    1217 = 13*93 + 8; hence not 13 divides 1217 by NAT_4:9;
    1217 = 17*71 + 10; hence not 17 divides 1217 by NAT_4:9;
    1217 = 19*64 + 1; hence not 19 divides 1217 by NAT_4:9;
    1217 = 23*52 + 21; hence not 23 divides 1217 by NAT_4:9;
    1217 = 29*41 + 28; hence not 29 divides 1217 by NAT_4:9;
    1217 = 31*39 + 8; hence not 31 divides 1217 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1217 & n is prime
  holds not n divides 1217 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
