
theorem
  4789 is prime
proof
  now
    4789 = 2*2394 + 1; hence not 2 divides 4789 by NAT_4:9;
    4789 = 3*1596 + 1; hence not 3 divides 4789 by NAT_4:9;
    4789 = 5*957 + 4; hence not 5 divides 4789 by NAT_4:9;
    4789 = 7*684 + 1; hence not 7 divides 4789 by NAT_4:9;
    4789 = 11*435 + 4; hence not 11 divides 4789 by NAT_4:9;
    4789 = 13*368 + 5; hence not 13 divides 4789 by NAT_4:9;
    4789 = 17*281 + 12; hence not 17 divides 4789 by NAT_4:9;
    4789 = 19*252 + 1; hence not 19 divides 4789 by NAT_4:9;
    4789 = 23*208 + 5; hence not 23 divides 4789 by NAT_4:9;
    4789 = 29*165 + 4; hence not 29 divides 4789 by NAT_4:9;
    4789 = 31*154 + 15; hence not 31 divides 4789 by NAT_4:9;
    4789 = 37*129 + 16; hence not 37 divides 4789 by NAT_4:9;
    4789 = 41*116 + 33; hence not 41 divides 4789 by NAT_4:9;
    4789 = 43*111 + 16; hence not 43 divides 4789 by NAT_4:9;
    4789 = 47*101 + 42; hence not 47 divides 4789 by NAT_4:9;
    4789 = 53*90 + 19; hence not 53 divides 4789 by NAT_4:9;
    4789 = 59*81 + 10; hence not 59 divides 4789 by NAT_4:9;
    4789 = 61*78 + 31; hence not 61 divides 4789 by NAT_4:9;
    4789 = 67*71 + 32; hence not 67 divides 4789 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4789 & n is prime
  holds not n divides 4789 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
