
theorem
  4787 is prime
proof
  now
    4787 = 2*2393 + 1; hence not 2 divides 4787 by NAT_4:9;
    4787 = 3*1595 + 2; hence not 3 divides 4787 by NAT_4:9;
    4787 = 5*957 + 2; hence not 5 divides 4787 by NAT_4:9;
    4787 = 7*683 + 6; hence not 7 divides 4787 by NAT_4:9;
    4787 = 11*435 + 2; hence not 11 divides 4787 by NAT_4:9;
    4787 = 13*368 + 3; hence not 13 divides 4787 by NAT_4:9;
    4787 = 17*281 + 10; hence not 17 divides 4787 by NAT_4:9;
    4787 = 19*251 + 18; hence not 19 divides 4787 by NAT_4:9;
    4787 = 23*208 + 3; hence not 23 divides 4787 by NAT_4:9;
    4787 = 29*165 + 2; hence not 29 divides 4787 by NAT_4:9;
    4787 = 31*154 + 13; hence not 31 divides 4787 by NAT_4:9;
    4787 = 37*129 + 14; hence not 37 divides 4787 by NAT_4:9;
    4787 = 41*116 + 31; hence not 41 divides 4787 by NAT_4:9;
    4787 = 43*111 + 14; hence not 43 divides 4787 by NAT_4:9;
    4787 = 47*101 + 40; hence not 47 divides 4787 by NAT_4:9;
    4787 = 53*90 + 17; hence not 53 divides 4787 by NAT_4:9;
    4787 = 59*81 + 8; hence not 59 divides 4787 by NAT_4:9;
    4787 = 61*78 + 29; hence not 61 divides 4787 by NAT_4:9;
    4787 = 67*71 + 30; hence not 67 divides 4787 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4787 & n is prime
  holds not n divides 4787 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
