
theorem
  1361 is prime
proof
  now
    1361 = 2*680 + 1; hence not 2 divides 1361 by NAT_4:9;
    1361 = 3*453 + 2; hence not 3 divides 1361 by NAT_4:9;
    1361 = 5*272 + 1; hence not 5 divides 1361 by NAT_4:9;
    1361 = 7*194 + 3; hence not 7 divides 1361 by NAT_4:9;
    1361 = 11*123 + 8; hence not 11 divides 1361 by NAT_4:9;
    1361 = 13*104 + 9; hence not 13 divides 1361 by NAT_4:9;
    1361 = 17*80 + 1; hence not 17 divides 1361 by NAT_4:9;
    1361 = 19*71 + 12; hence not 19 divides 1361 by NAT_4:9;
    1361 = 23*59 + 4; hence not 23 divides 1361 by NAT_4:9;
    1361 = 29*46 + 27; hence not 29 divides 1361 by NAT_4:9;
    1361 = 31*43 + 28; hence not 31 divides 1361 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1361 & n is prime
  holds not n divides 1361 by XPRIMET1:22;
  hence thesis by NAT_4:14;
