
theorem
  4783 is prime
proof
  now
    4783 = 2*2391 + 1; hence not 2 divides 4783 by NAT_4:9;
    4783 = 3*1594 + 1; hence not 3 divides 4783 by NAT_4:9;
    4783 = 5*956 + 3; hence not 5 divides 4783 by NAT_4:9;
    4783 = 7*683 + 2; hence not 7 divides 4783 by NAT_4:9;
    4783 = 11*434 + 9; hence not 11 divides 4783 by NAT_4:9;
    4783 = 13*367 + 12; hence not 13 divides 4783 by NAT_4:9;
    4783 = 17*281 + 6; hence not 17 divides 4783 by NAT_4:9;
    4783 = 19*251 + 14; hence not 19 divides 4783 by NAT_4:9;
    4783 = 23*207 + 22; hence not 23 divides 4783 by NAT_4:9;
    4783 = 29*164 + 27; hence not 29 divides 4783 by NAT_4:9;
    4783 = 31*154 + 9; hence not 31 divides 4783 by NAT_4:9;
    4783 = 37*129 + 10; hence not 37 divides 4783 by NAT_4:9;
    4783 = 41*116 + 27; hence not 41 divides 4783 by NAT_4:9;
    4783 = 43*111 + 10; hence not 43 divides 4783 by NAT_4:9;
    4783 = 47*101 + 36; hence not 47 divides 4783 by NAT_4:9;
    4783 = 53*90 + 13; hence not 53 divides 4783 by NAT_4:9;
    4783 = 59*81 + 4; hence not 59 divides 4783 by NAT_4:9;
    4783 = 61*78 + 25; hence not 61 divides 4783 by NAT_4:9;
    4783 = 67*71 + 26; hence not 67 divides 4783 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4783 & n is prime
  holds not n divides 4783 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
