
theorem
  4723 is prime
proof
  now
    4723 = 2*2361 + 1; hence not 2 divides 4723 by NAT_4:9;
    4723 = 3*1574 + 1; hence not 3 divides 4723 by NAT_4:9;
    4723 = 5*944 + 3; hence not 5 divides 4723 by NAT_4:9;
    4723 = 7*674 + 5; hence not 7 divides 4723 by NAT_4:9;
    4723 = 11*429 + 4; hence not 11 divides 4723 by NAT_4:9;
    4723 = 13*363 + 4; hence not 13 divides 4723 by NAT_4:9;
    4723 = 17*277 + 14; hence not 17 divides 4723 by NAT_4:9;
    4723 = 19*248 + 11; hence not 19 divides 4723 by NAT_4:9;
    4723 = 23*205 + 8; hence not 23 divides 4723 by NAT_4:9;
    4723 = 29*162 + 25; hence not 29 divides 4723 by NAT_4:9;
    4723 = 31*152 + 11; hence not 31 divides 4723 by NAT_4:9;
    4723 = 37*127 + 24; hence not 37 divides 4723 by NAT_4:9;
    4723 = 41*115 + 8; hence not 41 divides 4723 by NAT_4:9;
    4723 = 43*109 + 36; hence not 43 divides 4723 by NAT_4:9;
    4723 = 47*100 + 23; hence not 47 divides 4723 by NAT_4:9;
    4723 = 53*89 + 6; hence not 53 divides 4723 by NAT_4:9;
    4723 = 59*80 + 3; hence not 59 divides 4723 by NAT_4:9;
    4723 = 61*77 + 26; hence not 61 divides 4723 by NAT_4:9;
    4723 = 67*70 + 33; hence not 67 divides 4723 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4723 & n is prime
  holds not n divides 4723 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
