9133 = (2 * 4566) + 1 ;
hence not 2 divides 9133 by NAT_4:9; :: thesis:
9133 = (3 * 3044) + 1 ;
hence not 3 divides 9133 by NAT_4:9; :: thesis:
9133 = (5 * 1826) + 3 ;
hence not 5 divides 9133 by NAT_4:9; :: thesis:
9133 = (7 * 1304) + 5 ;
hence not 7 divides 9133 by NAT_4:9; :: thesis:
9133 = (11 * 830) + 3 ;
hence not 11 divides 9133 by NAT_4:9; :: thesis:
9133 = (13 * 702) + 7 ;
hence not 13 divides 9133 by NAT_4:9; :: thesis:
9133 = (17 * 537) + 4 ;
hence not 17 divides 9133 by NAT_4:9; :: thesis:
9133 = (19 * 480) + 13 ;
hence not 19 divides 9133 by NAT_4:9; :: thesis:
9133 = (23 * 397) + 2 ;
hence not 23 divides 9133 by NAT_4:9; :: thesis:
9133 = (29 * 314) + 27 ;
hence not 29 divides 9133 by NAT_4:9; :: thesis:
9133 = (31 * 294) + 19 ;
hence not 31 divides 9133 by NAT_4:9; :: thesis:
9133 = (37 * 246) + 31 ;
hence not 37 divides 9133 by NAT_4:9; :: thesis:
9133 = (41 * 222) + 31 ;
hence not 41 divides 9133 by NAT_4:9; :: thesis:
9133 = (43 * 212) + 17 ;
hence not 43 divides 9133 by NAT_4:9; :: thesis:
9133 = (47 * 194) + 15 ;
hence not 47 divides 9133 by NAT_4:9; :: thesis:
9133 = (53 * 172) + 17 ;
hence not 53 divides 9133 by NAT_4:9; :: thesis:
9133 = (59 * 154) + 47 ;
hence not 59 divides 9133 by NAT_4:9; :: thesis:
9133 = (61 * 149) + 44 ;
hence not 61 divides 9133 by NAT_4:9; :: thesis:
9133 = (67 * 136) + 21 ;
hence not 67 divides 9133 by NAT_4:9; :: thesis:
9133 = (71 * 128) + 45 ;
hence not 71 divides 9133 by NAT_4:9; :: thesis:
9133 = (73 * 125) + 8 ;
hence not 73 divides 9133 by NAT_4:9; :: thesis:
9133 = (79 * 115) + 48 ;
hence not 79 divides 9133 by NAT_4:9; :: thesis:
9133 = (83 * 110) + 3 ;
hence not 83 divides 9133 by NAT_4:9; :: thesis:
9133 = (89 * 102) + 55 ;
hence not 89 divides 9133 by NAT_4:9; :: thesis:

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 9133 is prime by NAT_4:14; :: thesis: