
theorem
  4441 is prime
proof
  now
    4441 = 2*2220 + 1; hence not 2 divides 4441 by NAT_4:9;
    4441 = 3*1480 + 1; hence not 3 divides 4441 by NAT_4:9;
    4441 = 5*888 + 1; hence not 5 divides 4441 by NAT_4:9;
    4441 = 7*634 + 3; hence not 7 divides 4441 by NAT_4:9;
    4441 = 11*403 + 8; hence not 11 divides 4441 by NAT_4:9;
    4441 = 13*341 + 8; hence not 13 divides 4441 by NAT_4:9;
    4441 = 17*261 + 4; hence not 17 divides 4441 by NAT_4:9;
    4441 = 19*233 + 14; hence not 19 divides 4441 by NAT_4:9;
    4441 = 23*193 + 2; hence not 23 divides 4441 by NAT_4:9;
    4441 = 29*153 + 4; hence not 29 divides 4441 by NAT_4:9;
    4441 = 31*143 + 8; hence not 31 divides 4441 by NAT_4:9;
    4441 = 37*120 + 1; hence not 37 divides 4441 by NAT_4:9;
    4441 = 41*108 + 13; hence not 41 divides 4441 by NAT_4:9;
    4441 = 43*103 + 12; hence not 43 divides 4441 by NAT_4:9;
    4441 = 47*94 + 23; hence not 47 divides 4441 by NAT_4:9;
    4441 = 53*83 + 42; hence not 53 divides 4441 by NAT_4:9;
    4441 = 59*75 + 16; hence not 59 divides 4441 by NAT_4:9;
    4441 = 61*72 + 49; hence not 61 divides 4441 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4441 & n is prime
  holds not n divides 4441 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
