
theorem
  4909 is prime
proof
  now
    4909 = 2*2454 + 1; hence not 2 divides 4909 by NAT_4:9;
    4909 = 3*1636 + 1; hence not 3 divides 4909 by NAT_4:9;
    4909 = 5*981 + 4; hence not 5 divides 4909 by NAT_4:9;
    4909 = 7*701 + 2; hence not 7 divides 4909 by NAT_4:9;
    4909 = 11*446 + 3; hence not 11 divides 4909 by NAT_4:9;
    4909 = 13*377 + 8; hence not 13 divides 4909 by NAT_4:9;
    4909 = 17*288 + 13; hence not 17 divides 4909 by NAT_4:9;
    4909 = 19*258 + 7; hence not 19 divides 4909 by NAT_4:9;
    4909 = 23*213 + 10; hence not 23 divides 4909 by NAT_4:9;
    4909 = 29*169 + 8; hence not 29 divides 4909 by NAT_4:9;
    4909 = 31*158 + 11; hence not 31 divides 4909 by NAT_4:9;
    4909 = 37*132 + 25; hence not 37 divides 4909 by NAT_4:9;
    4909 = 41*119 + 30; hence not 41 divides 4909 by NAT_4:9;
    4909 = 43*114 + 7; hence not 43 divides 4909 by NAT_4:9;
    4909 = 47*104 + 21; hence not 47 divides 4909 by NAT_4:9;
    4909 = 53*92 + 33; hence not 53 divides 4909 by NAT_4:9;
    4909 = 59*83 + 12; hence not 59 divides 4909 by NAT_4:9;
    4909 = 61*80 + 29; hence not 61 divides 4909 by NAT_4:9;
    4909 = 67*73 + 18; hence not 67 divides 4909 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4909 & n is prime
  holds not n divides 4909 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
