
theorem
  4397 is prime
proof
  now
    4397 = 2*2198 + 1; hence not 2 divides 4397 by NAT_4:9;
    4397 = 3*1465 + 2; hence not 3 divides 4397 by NAT_4:9;
    4397 = 5*879 + 2; hence not 5 divides 4397 by NAT_4:9;
    4397 = 7*628 + 1; hence not 7 divides 4397 by NAT_4:9;
    4397 = 11*399 + 8; hence not 11 divides 4397 by NAT_4:9;
    4397 = 13*338 + 3; hence not 13 divides 4397 by NAT_4:9;
    4397 = 17*258 + 11; hence not 17 divides 4397 by NAT_4:9;
    4397 = 19*231 + 8; hence not 19 divides 4397 by NAT_4:9;
    4397 = 23*191 + 4; hence not 23 divides 4397 by NAT_4:9;
    4397 = 29*151 + 18; hence not 29 divides 4397 by NAT_4:9;
    4397 = 31*141 + 26; hence not 31 divides 4397 by NAT_4:9;
    4397 = 37*118 + 31; hence not 37 divides 4397 by NAT_4:9;
    4397 = 41*107 + 10; hence not 41 divides 4397 by NAT_4:9;
    4397 = 43*102 + 11; hence not 43 divides 4397 by NAT_4:9;
    4397 = 47*93 + 26; hence not 47 divides 4397 by NAT_4:9;
    4397 = 53*82 + 51; hence not 53 divides 4397 by NAT_4:9;
    4397 = 59*74 + 31; hence not 59 divides 4397 by NAT_4:9;
    4397 = 61*72 + 5; hence not 61 divides 4397 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4397 & n is prime
  holds not n divides 4397 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
