
theorem
  9967 is prime
proof
  now
    9967 = 2*4983 + 1; hence not 2 divides 9967 by NAT_4:9;
    9967 = 3*3322 + 1; hence not 3 divides 9967 by NAT_4:9;
    9967 = 5*1993 + 2; hence not 5 divides 9967 by NAT_4:9;
    9967 = 7*1423 + 6; hence not 7 divides 9967 by NAT_4:9;
    9967 = 11*906 + 1; hence not 11 divides 9967 by NAT_4:9;
    9967 = 13*766 + 9; hence not 13 divides 9967 by NAT_4:9;
    9967 = 17*586 + 5; hence not 17 divides 9967 by NAT_4:9;
    9967 = 19*524 + 11; hence not 19 divides 9967 by NAT_4:9;
    9967 = 23*433 + 8; hence not 23 divides 9967 by NAT_4:9;
    9967 = 29*343 + 20; hence not 29 divides 9967 by NAT_4:9;
    9967 = 31*321 + 16; hence not 31 divides 9967 by NAT_4:9;
    9967 = 37*269 + 14; hence not 37 divides 9967 by NAT_4:9;
    9967 = 41*243 + 4; hence not 41 divides 9967 by NAT_4:9;
    9967 = 43*231 + 34; hence not 43 divides 9967 by NAT_4:9;
    9967 = 47*212 + 3; hence not 47 divides 9967 by NAT_4:9;
    9967 = 53*188 + 3; hence not 53 divides 9967 by NAT_4:9;
    9967 = 59*168 + 55; hence not 59 divides 9967 by NAT_4:9;
    9967 = 61*163 + 24; hence not 61 divides 9967 by NAT_4:9;
    9967 = 67*148 + 51; hence not 67 divides 9967 by NAT_4:9;
    9967 = 71*140 + 27; hence not 71 divides 9967 by NAT_4:9;
    9967 = 73*136 + 39; hence not 73 divides 9967 by NAT_4:9;
    9967 = 79*126 + 13; hence not 79 divides 9967 by NAT_4:9;
    9967 = 83*120 + 7; hence not 83 divides 9967 by NAT_4:9;
    9967 = 89*111 + 88; hence not 89 divides 9967 by NAT_4:9;
    9967 = 97*102 + 73; hence not 97 divides 9967 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9967 & n is prime
  holds not n divides 9967 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
