
theorem
  9133 is prime
proof
  now
    9133 = 2*4566 + 1; hence not 2 divides 9133 by NAT_4:9;
    9133 = 3*3044 + 1; hence not 3 divides 9133 by NAT_4:9;
    9133 = 5*1826 + 3; hence not 5 divides 9133 by NAT_4:9;
    9133 = 7*1304 + 5; hence not 7 divides 9133 by NAT_4:9;
    9133 = 11*830 + 3; hence not 11 divides 9133 by NAT_4:9;
    9133 = 13*702 + 7; hence not 13 divides 9133 by NAT_4:9;
    9133 = 17*537 + 4; hence not 17 divides 9133 by NAT_4:9;
    9133 = 19*480 + 13; hence not 19 divides 9133 by NAT_4:9;
    9133 = 23*397 + 2; hence not 23 divides 9133 by NAT_4:9;
    9133 = 29*314 + 27; hence not 29 divides 9133 by NAT_4:9;
    9133 = 31*294 + 19; hence not 31 divides 9133 by NAT_4:9;
    9133 = 37*246 + 31; hence not 37 divides 9133 by NAT_4:9;
    9133 = 41*222 + 31; hence not 41 divides 9133 by NAT_4:9;
    9133 = 43*212 + 17; hence not 43 divides 9133 by NAT_4:9;
    9133 = 47*194 + 15; hence not 47 divides 9133 by NAT_4:9;
    9133 = 53*172 + 17; hence not 53 divides 9133 by NAT_4:9;
    9133 = 59*154 + 47; hence not 59 divides 9133 by NAT_4:9;
    9133 = 61*149 + 44; hence not 61 divides 9133 by NAT_4:9;
    9133 = 67*136 + 21; hence not 67 divides 9133 by NAT_4:9;
    9133 = 71*128 + 45; hence not 71 divides 9133 by NAT_4:9;
    9133 = 73*125 + 8; hence not 73 divides 9133 by NAT_4:9;
    9133 = 79*115 + 48; hence not 79 divides 9133 by NAT_4:9;
    9133 = 83*110 + 3; hence not 83 divides 9133 by NAT_4:9;
    9133 = 89*102 + 55; hence not 89 divides 9133 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9133 & n is prime
  holds not n divides 9133 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
