
theorem
  9491 is prime
proof
  now
    9491 = 2*4745 + 1; hence not 2 divides 9491 by NAT_4:9;
    9491 = 3*3163 + 2; hence not 3 divides 9491 by NAT_4:9;
    9491 = 5*1898 + 1; hence not 5 divides 9491 by NAT_4:9;
    9491 = 7*1355 + 6; hence not 7 divides 9491 by NAT_4:9;
    9491 = 11*862 + 9; hence not 11 divides 9491 by NAT_4:9;
    9491 = 13*730 + 1; hence not 13 divides 9491 by NAT_4:9;
    9491 = 17*558 + 5; hence not 17 divides 9491 by NAT_4:9;
    9491 = 19*499 + 10; hence not 19 divides 9491 by NAT_4:9;
    9491 = 23*412 + 15; hence not 23 divides 9491 by NAT_4:9;
    9491 = 29*327 + 8; hence not 29 divides 9491 by NAT_4:9;
    9491 = 31*306 + 5; hence not 31 divides 9491 by NAT_4:9;
    9491 = 37*256 + 19; hence not 37 divides 9491 by NAT_4:9;
    9491 = 41*231 + 20; hence not 41 divides 9491 by NAT_4:9;
    9491 = 43*220 + 31; hence not 43 divides 9491 by NAT_4:9;
    9491 = 47*201 + 44; hence not 47 divides 9491 by NAT_4:9;
    9491 = 53*179 + 4; hence not 53 divides 9491 by NAT_4:9;
    9491 = 59*160 + 51; hence not 59 divides 9491 by NAT_4:9;
    9491 = 61*155 + 36; hence not 61 divides 9491 by NAT_4:9;
    9491 = 67*141 + 44; hence not 67 divides 9491 by NAT_4:9;
    9491 = 71*133 + 48; hence not 71 divides 9491 by NAT_4:9;
    9491 = 73*130 + 1; hence not 73 divides 9491 by NAT_4:9;
    9491 = 79*120 + 11; hence not 79 divides 9491 by NAT_4:9;
    9491 = 83*114 + 29; hence not 83 divides 9491 by NAT_4:9;
    9491 = 89*106 + 57; hence not 89 divides 9491 by NAT_4:9;
    9491 = 97*97 + 82; hence not 97 divides 9491 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9491 & n is prime
  holds not n divides 9491 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
