
theorem
  4871 is prime
proof
  now
    4871 = 2*2435 + 1; hence not 2 divides 4871 by NAT_4:9;
    4871 = 3*1623 + 2; hence not 3 divides 4871 by NAT_4:9;
    4871 = 5*974 + 1; hence not 5 divides 4871 by NAT_4:9;
    4871 = 7*695 + 6; hence not 7 divides 4871 by NAT_4:9;
    4871 = 11*442 + 9; hence not 11 divides 4871 by NAT_4:9;
    4871 = 13*374 + 9; hence not 13 divides 4871 by NAT_4:9;
    4871 = 17*286 + 9; hence not 17 divides 4871 by NAT_4:9;
    4871 = 19*256 + 7; hence not 19 divides 4871 by NAT_4:9;
    4871 = 23*211 + 18; hence not 23 divides 4871 by NAT_4:9;
    4871 = 29*167 + 28; hence not 29 divides 4871 by NAT_4:9;
    4871 = 31*157 + 4; hence not 31 divides 4871 by NAT_4:9;
    4871 = 37*131 + 24; hence not 37 divides 4871 by NAT_4:9;
    4871 = 41*118 + 33; hence not 41 divides 4871 by NAT_4:9;
    4871 = 43*113 + 12; hence not 43 divides 4871 by NAT_4:9;
    4871 = 47*103 + 30; hence not 47 divides 4871 by NAT_4:9;
    4871 = 53*91 + 48; hence not 53 divides 4871 by NAT_4:9;
    4871 = 59*82 + 33; hence not 59 divides 4871 by NAT_4:9;
    4871 = 61*79 + 52; hence not 61 divides 4871 by NAT_4:9;
    4871 = 67*72 + 47; hence not 67 divides 4871 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4871 & n is prime
  holds not n divides 4871 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
