
theorem
  4733 is prime
proof
  now
    4733 = 2*2366 + 1; hence not 2 divides 4733 by NAT_4:9;
    4733 = 3*1577 + 2; hence not 3 divides 4733 by NAT_4:9;
    4733 = 5*946 + 3; hence not 5 divides 4733 by NAT_4:9;
    4733 = 7*676 + 1; hence not 7 divides 4733 by NAT_4:9;
    4733 = 11*430 + 3; hence not 11 divides 4733 by NAT_4:9;
    4733 = 13*364 + 1; hence not 13 divides 4733 by NAT_4:9;
    4733 = 17*278 + 7; hence not 17 divides 4733 by NAT_4:9;
    4733 = 19*249 + 2; hence not 19 divides 4733 by NAT_4:9;
    4733 = 23*205 + 18; hence not 23 divides 4733 by NAT_4:9;
    4733 = 29*163 + 6; hence not 29 divides 4733 by NAT_4:9;
    4733 = 31*152 + 21; hence not 31 divides 4733 by NAT_4:9;
    4733 = 37*127 + 34; hence not 37 divides 4733 by NAT_4:9;
    4733 = 41*115 + 18; hence not 41 divides 4733 by NAT_4:9;
    4733 = 43*110 + 3; hence not 43 divides 4733 by NAT_4:9;
    4733 = 47*100 + 33; hence not 47 divides 4733 by NAT_4:9;
    4733 = 53*89 + 16; hence not 53 divides 4733 by NAT_4:9;
    4733 = 59*80 + 13; hence not 59 divides 4733 by NAT_4:9;
    4733 = 61*77 + 36; hence not 61 divides 4733 by NAT_4:9;
    4733 = 67*70 + 43; hence not 67 divides 4733 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4733 & n is prime
  holds not n divides 4733 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
