9043 = (2 * 4521) + 1 ;
hence not 2 divides 9043 by NAT_4:9; :: thesis:
9043 = (3 * 3014) + 1 ;
hence not 3 divides 9043 by NAT_4:9; :: thesis:
9043 = (5 * 1808) + 3 ;
hence not 5 divides 9043 by NAT_4:9; :: thesis:
9043 = (7 * 1291) + 6 ;
hence not 7 divides 9043 by NAT_4:9; :: thesis:
9043 = (11 * 822) + 1 ;
hence not 11 divides 9043 by NAT_4:9; :: thesis:
9043 = (13 * 695) + 8 ;
hence not 13 divides 9043 by NAT_4:9; :: thesis:
9043 = (17 * 531) + 16 ;
hence not 17 divides 9043 by NAT_4:9; :: thesis:
9043 = (19 * 475) + 18 ;
hence not 19 divides 9043 by NAT_4:9; :: thesis:
9043 = (23 * 393) + 4 ;
hence not 23 divides 9043 by NAT_4:9; :: thesis:
9043 = (29 * 311) + 24 ;
hence not 29 divides 9043 by NAT_4:9; :: thesis:
9043 = (31 * 291) + 22 ;
hence not 31 divides 9043 by NAT_4:9; :: thesis:
9043 = (37 * 244) + 15 ;
hence not 37 divides 9043 by NAT_4:9; :: thesis:
9043 = (41 * 220) + 23 ;
hence not 41 divides 9043 by NAT_4:9; :: thesis:
9043 = (43 * 210) + 13 ;
hence not 43 divides 9043 by NAT_4:9; :: thesis:
9043 = (47 * 192) + 19 ;
hence not 47 divides 9043 by NAT_4:9; :: thesis:
9043 = (53 * 170) + 33 ;
hence not 53 divides 9043 by NAT_4:9; :: thesis:
9043 = (59 * 153) + 16 ;
hence not 59 divides 9043 by NAT_4:9; :: thesis:
9043 = (61 * 148) + 15 ;
hence not 61 divides 9043 by NAT_4:9; :: thesis:
9043 = (67 * 134) + 65 ;
hence not 67 divides 9043 by NAT_4:9; :: thesis:
9043 = (71 * 127) + 26 ;
hence not 71 divides 9043 by NAT_4:9; :: thesis:
9043 = (73 * 123) + 64 ;
hence not 73 divides 9043 by NAT_4:9; :: thesis:
9043 = (79 * 114) + 37 ;
hence not 79 divides 9043 by NAT_4:9; :: thesis:
9043 = (83 * 108) + 79 ;
hence not 83 divides 9043 by NAT_4:9; :: thesis:
9043 = (89 * 101) + 54 ;
hence not 89 divides 9043 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9043 & n is prime holds
not n divides 9043 by XPRIMET1:48;
hence 9043 is prime by NAT_4:14; :: thesis: