
theorem
  4447 is prime
proof
  now
    4447 = 2*2223 + 1; hence not 2 divides 4447 by NAT_4:9;
    4447 = 3*1482 + 1; hence not 3 divides 4447 by NAT_4:9;
    4447 = 5*889 + 2; hence not 5 divides 4447 by NAT_4:9;
    4447 = 7*635 + 2; hence not 7 divides 4447 by NAT_4:9;
    4447 = 11*404 + 3; hence not 11 divides 4447 by NAT_4:9;
    4447 = 13*342 + 1; hence not 13 divides 4447 by NAT_4:9;
    4447 = 17*261 + 10; hence not 17 divides 4447 by NAT_4:9;
    4447 = 19*234 + 1; hence not 19 divides 4447 by NAT_4:9;
    4447 = 23*193 + 8; hence not 23 divides 4447 by NAT_4:9;
    4447 = 29*153 + 10; hence not 29 divides 4447 by NAT_4:9;
    4447 = 31*143 + 14; hence not 31 divides 4447 by NAT_4:9;
    4447 = 37*120 + 7; hence not 37 divides 4447 by NAT_4:9;
    4447 = 41*108 + 19; hence not 41 divides 4447 by NAT_4:9;
    4447 = 43*103 + 18; hence not 43 divides 4447 by NAT_4:9;
    4447 = 47*94 + 29; hence not 47 divides 4447 by NAT_4:9;
    4447 = 53*83 + 48; hence not 53 divides 4447 by NAT_4:9;
    4447 = 59*75 + 22; hence not 59 divides 4447 by NAT_4:9;
    4447 = 61*72 + 55; hence not 61 divides 4447 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4447 & n is prime
  holds not n divides 4447 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
