
theorem
  9623 is prime
proof
  now
    9623 = 2*4811 + 1; hence not 2 divides 9623 by NAT_4:9;
    9623 = 3*3207 + 2; hence not 3 divides 9623 by NAT_4:9;
    9623 = 5*1924 + 3; hence not 5 divides 9623 by NAT_4:9;
    9623 = 7*1374 + 5; hence not 7 divides 9623 by NAT_4:9;
    9623 = 11*874 + 9; hence not 11 divides 9623 by NAT_4:9;
    9623 = 13*740 + 3; hence not 13 divides 9623 by NAT_4:9;
    9623 = 17*566 + 1; hence not 17 divides 9623 by NAT_4:9;
    9623 = 19*506 + 9; hence not 19 divides 9623 by NAT_4:9;
    9623 = 23*418 + 9; hence not 23 divides 9623 by NAT_4:9;
    9623 = 29*331 + 24; hence not 29 divides 9623 by NAT_4:9;
    9623 = 31*310 + 13; hence not 31 divides 9623 by NAT_4:9;
    9623 = 37*260 + 3; hence not 37 divides 9623 by NAT_4:9;
    9623 = 41*234 + 29; hence not 41 divides 9623 by NAT_4:9;
    9623 = 43*223 + 34; hence not 43 divides 9623 by NAT_4:9;
    9623 = 47*204 + 35; hence not 47 divides 9623 by NAT_4:9;
    9623 = 53*181 + 30; hence not 53 divides 9623 by NAT_4:9;
    9623 = 59*163 + 6; hence not 59 divides 9623 by NAT_4:9;
    9623 = 61*157 + 46; hence not 61 divides 9623 by NAT_4:9;
    9623 = 67*143 + 42; hence not 67 divides 9623 by NAT_4:9;
    9623 = 71*135 + 38; hence not 71 divides 9623 by NAT_4:9;
    9623 = 73*131 + 60; hence not 73 divides 9623 by NAT_4:9;
    9623 = 79*121 + 64; hence not 79 divides 9623 by NAT_4:9;
    9623 = 83*115 + 78; hence not 83 divides 9623 by NAT_4:9;
    9623 = 89*108 + 11; hence not 89 divides 9623 by NAT_4:9;
    9623 = 97*99 + 20; hence not 97 divides 9623 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9623 & n is prime
  holds not n divides 9623 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
