
theorem
  4877 is prime
proof
  now
    4877 = 2*2438 + 1; hence not 2 divides 4877 by NAT_4:9;
    4877 = 3*1625 + 2; hence not 3 divides 4877 by NAT_4:9;
    4877 = 5*975 + 2; hence not 5 divides 4877 by NAT_4:9;
    4877 = 7*696 + 5; hence not 7 divides 4877 by NAT_4:9;
    4877 = 11*443 + 4; hence not 11 divides 4877 by NAT_4:9;
    4877 = 13*375 + 2; hence not 13 divides 4877 by NAT_4:9;
    4877 = 17*286 + 15; hence not 17 divides 4877 by NAT_4:9;
    4877 = 19*256 + 13; hence not 19 divides 4877 by NAT_4:9;
    4877 = 23*212 + 1; hence not 23 divides 4877 by NAT_4:9;
    4877 = 29*168 + 5; hence not 29 divides 4877 by NAT_4:9;
    4877 = 31*157 + 10; hence not 31 divides 4877 by NAT_4:9;
    4877 = 37*131 + 30; hence not 37 divides 4877 by NAT_4:9;
    4877 = 41*118 + 39; hence not 41 divides 4877 by NAT_4:9;
    4877 = 43*113 + 18; hence not 43 divides 4877 by NAT_4:9;
    4877 = 47*103 + 36; hence not 47 divides 4877 by NAT_4:9;
    4877 = 53*92 + 1; hence not 53 divides 4877 by NAT_4:9;
    4877 = 59*82 + 39; hence not 59 divides 4877 by NAT_4:9;
    4877 = 61*79 + 58; hence not 61 divides 4877 by NAT_4:9;
    4877 = 67*72 + 53; hence not 67 divides 4877 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4877 & n is prime
  holds not n divides 4877 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
