
theorem
  7723 is prime
proof
  now
    7723 = 2*3861 + 1; hence not 2 divides 7723 by NAT_4:9;
    7723 = 3*2574 + 1; hence not 3 divides 7723 by NAT_4:9;
    7723 = 5*1544 + 3; hence not 5 divides 7723 by NAT_4:9;
    7723 = 7*1103 + 2; hence not 7 divides 7723 by NAT_4:9;
    7723 = 11*702 + 1; hence not 11 divides 7723 by NAT_4:9;
    7723 = 13*594 + 1; hence not 13 divides 7723 by NAT_4:9;
    7723 = 17*454 + 5; hence not 17 divides 7723 by NAT_4:9;
    7723 = 19*406 + 9; hence not 19 divides 7723 by NAT_4:9;
    7723 = 23*335 + 18; hence not 23 divides 7723 by NAT_4:9;
    7723 = 29*266 + 9; hence not 29 divides 7723 by NAT_4:9;
    7723 = 31*249 + 4; hence not 31 divides 7723 by NAT_4:9;
    7723 = 37*208 + 27; hence not 37 divides 7723 by NAT_4:9;
    7723 = 41*188 + 15; hence not 41 divides 7723 by NAT_4:9;
    7723 = 43*179 + 26; hence not 43 divides 7723 by NAT_4:9;
    7723 = 47*164 + 15; hence not 47 divides 7723 by NAT_4:9;
    7723 = 53*145 + 38; hence not 53 divides 7723 by NAT_4:9;
    7723 = 59*130 + 53; hence not 59 divides 7723 by NAT_4:9;
    7723 = 61*126 + 37; hence not 61 divides 7723 by NAT_4:9;
    7723 = 67*115 + 18; hence not 67 divides 7723 by NAT_4:9;
    7723 = 71*108 + 55; hence not 71 divides 7723 by NAT_4:9;
    7723 = 73*105 + 58; hence not 73 divides 7723 by NAT_4:9;
    7723 = 79*97 + 60; hence not 79 divides 7723 by NAT_4:9;
    7723 = 83*93 + 4; hence not 83 divides 7723 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7723 & n is prime
  holds not n divides 7723 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
