
theorem
  4903 is prime
proof
  now
    4903 = 2*2451 + 1; hence not 2 divides 4903 by NAT_4:9;
    4903 = 3*1634 + 1; hence not 3 divides 4903 by NAT_4:9;
    4903 = 5*980 + 3; hence not 5 divides 4903 by NAT_4:9;
    4903 = 7*700 + 3; hence not 7 divides 4903 by NAT_4:9;
    4903 = 11*445 + 8; hence not 11 divides 4903 by NAT_4:9;
    4903 = 13*377 + 2; hence not 13 divides 4903 by NAT_4:9;
    4903 = 17*288 + 7; hence not 17 divides 4903 by NAT_4:9;
    4903 = 19*258 + 1; hence not 19 divides 4903 by NAT_4:9;
    4903 = 23*213 + 4; hence not 23 divides 4903 by NAT_4:9;
    4903 = 29*169 + 2; hence not 29 divides 4903 by NAT_4:9;
    4903 = 31*158 + 5; hence not 31 divides 4903 by NAT_4:9;
    4903 = 37*132 + 19; hence not 37 divides 4903 by NAT_4:9;
    4903 = 41*119 + 24; hence not 41 divides 4903 by NAT_4:9;
    4903 = 43*114 + 1; hence not 43 divides 4903 by NAT_4:9;
    4903 = 47*104 + 15; hence not 47 divides 4903 by NAT_4:9;
    4903 = 53*92 + 27; hence not 53 divides 4903 by NAT_4:9;
    4903 = 59*83 + 6; hence not 59 divides 4903 by NAT_4:9;
    4903 = 61*80 + 23; hence not 61 divides 4903 by NAT_4:9;
    4903 = 67*73 + 12; hence not 67 divides 4903 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4903 & n is prime
  holds not n divides 4903 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
