
theorem
  1367 is prime
proof
  now
    1367 = 2*683 + 1; hence not 2 divides 1367 by NAT_4:9;
    1367 = 3*455 + 2; hence not 3 divides 1367 by NAT_4:9;
    1367 = 5*273 + 2; hence not 5 divides 1367 by NAT_4:9;
    1367 = 7*195 + 2; hence not 7 divides 1367 by NAT_4:9;
    1367 = 11*124 + 3; hence not 11 divides 1367 by NAT_4:9;
    1367 = 13*105 + 2; hence not 13 divides 1367 by NAT_4:9;
    1367 = 17*80 + 7; hence not 17 divides 1367 by NAT_4:9;
    1367 = 19*71 + 18; hence not 19 divides 1367 by NAT_4:9;
    1367 = 23*59 + 10; hence not 23 divides 1367 by NAT_4:9;
    1367 = 29*47 + 4; hence not 29 divides 1367 by NAT_4:9;
    1367 = 31*44 + 3; hence not 31 divides 1367 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1367 & n is prime
  holds not n divides 1367 by XPRIMET1:22;
  hence thesis by NAT_4:14;
