
theorem
  9661 is prime
proof
  now
    9661 = 2*4830 + 1; hence not 2 divides 9661 by NAT_4:9;
    9661 = 3*3220 + 1; hence not 3 divides 9661 by NAT_4:9;
    9661 = 5*1932 + 1; hence not 5 divides 9661 by NAT_4:9;
    9661 = 7*1380 + 1; hence not 7 divides 9661 by NAT_4:9;
    9661 = 11*878 + 3; hence not 11 divides 9661 by NAT_4:9;
    9661 = 13*743 + 2; hence not 13 divides 9661 by NAT_4:9;
    9661 = 17*568 + 5; hence not 17 divides 9661 by NAT_4:9;
    9661 = 19*508 + 9; hence not 19 divides 9661 by NAT_4:9;
    9661 = 23*420 + 1; hence not 23 divides 9661 by NAT_4:9;
    9661 = 29*333 + 4; hence not 29 divides 9661 by NAT_4:9;
    9661 = 31*311 + 20; hence not 31 divides 9661 by NAT_4:9;
    9661 = 37*261 + 4; hence not 37 divides 9661 by NAT_4:9;
    9661 = 41*235 + 26; hence not 41 divides 9661 by NAT_4:9;
    9661 = 43*224 + 29; hence not 43 divides 9661 by NAT_4:9;
    9661 = 47*205 + 26; hence not 47 divides 9661 by NAT_4:9;
    9661 = 53*182 + 15; hence not 53 divides 9661 by NAT_4:9;
    9661 = 59*163 + 44; hence not 59 divides 9661 by NAT_4:9;
    9661 = 61*158 + 23; hence not 61 divides 9661 by NAT_4:9;
    9661 = 67*144 + 13; hence not 67 divides 9661 by NAT_4:9;
    9661 = 71*136 + 5; hence not 71 divides 9661 by NAT_4:9;
    9661 = 73*132 + 25; hence not 73 divides 9661 by NAT_4:9;
    9661 = 79*122 + 23; hence not 79 divides 9661 by NAT_4:9;
    9661 = 83*116 + 33; hence not 83 divides 9661 by NAT_4:9;
    9661 = 89*108 + 49; hence not 89 divides 9661 by NAT_4:9;
    9661 = 97*99 + 58; hence not 97 divides 9661 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9661 & n is prime
  holds not n divides 9661 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
