
theorem
  9643 is prime
proof
  now
    9643 = 2*4821 + 1; hence not 2 divides 9643 by NAT_4:9;
    9643 = 3*3214 + 1; hence not 3 divides 9643 by NAT_4:9;
    9643 = 5*1928 + 3; hence not 5 divides 9643 by NAT_4:9;
    9643 = 7*1377 + 4; hence not 7 divides 9643 by NAT_4:9;
    9643 = 11*876 + 7; hence not 11 divides 9643 by NAT_4:9;
    9643 = 13*741 + 10; hence not 13 divides 9643 by NAT_4:9;
    9643 = 17*567 + 4; hence not 17 divides 9643 by NAT_4:9;
    9643 = 19*507 + 10; hence not 19 divides 9643 by NAT_4:9;
    9643 = 23*419 + 6; hence not 23 divides 9643 by NAT_4:9;
    9643 = 29*332 + 15; hence not 29 divides 9643 by NAT_4:9;
    9643 = 31*311 + 2; hence not 31 divides 9643 by NAT_4:9;
    9643 = 37*260 + 23; hence not 37 divides 9643 by NAT_4:9;
    9643 = 41*235 + 8; hence not 41 divides 9643 by NAT_4:9;
    9643 = 43*224 + 11; hence not 43 divides 9643 by NAT_4:9;
    9643 = 47*205 + 8; hence not 47 divides 9643 by NAT_4:9;
    9643 = 53*181 + 50; hence not 53 divides 9643 by NAT_4:9;
    9643 = 59*163 + 26; hence not 59 divides 9643 by NAT_4:9;
    9643 = 61*158 + 5; hence not 61 divides 9643 by NAT_4:9;
    9643 = 67*143 + 62; hence not 67 divides 9643 by NAT_4:9;
    9643 = 71*135 + 58; hence not 71 divides 9643 by NAT_4:9;
    9643 = 73*132 + 7; hence not 73 divides 9643 by NAT_4:9;
    9643 = 79*122 + 5; hence not 79 divides 9643 by NAT_4:9;
    9643 = 83*116 + 15; hence not 83 divides 9643 by NAT_4:9;
    9643 = 89*108 + 31; hence not 89 divides 9643 by NAT_4:9;
    9643 = 97*99 + 40; hence not 97 divides 9643 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9643 & n is prime
  holds not n divides 9643 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
