
theorem
  1381 is prime
proof
  now
    1381 = 2*690 + 1; hence not 2 divides 1381 by NAT_4:9;
    1381 = 3*460 + 1; hence not 3 divides 1381 by NAT_4:9;
    1381 = 5*276 + 1; hence not 5 divides 1381 by NAT_4:9;
    1381 = 7*197 + 2; hence not 7 divides 1381 by NAT_4:9;
    1381 = 11*125 + 6; hence not 11 divides 1381 by NAT_4:9;
    1381 = 13*106 + 3; hence not 13 divides 1381 by NAT_4:9;
    1381 = 17*81 + 4; hence not 17 divides 1381 by NAT_4:9;
    1381 = 19*72 + 13; hence not 19 divides 1381 by NAT_4:9;
    1381 = 23*60 + 1; hence not 23 divides 1381 by NAT_4:9;
    1381 = 29*47 + 18; hence not 29 divides 1381 by NAT_4:9;
    1381 = 31*44 + 17; hence not 31 divides 1381 by NAT_4:9;
    1381 = 37*37 + 12; hence not 37 divides 1381 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1381 & n is prime
  holds not n divides 1381 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
