9227 = (2 * 4613) + 1 ;
hence not 2 divides 9227 by NAT_4:9; :: thesis:
9227 = (3 * 3075) + 2 ;
hence not 3 divides 9227 by NAT_4:9; :: thesis:
9227 = (5 * 1845) + 2 ;
hence not 5 divides 9227 by NAT_4:9; :: thesis:
9227 = (7 * 1318) + 1 ;
hence not 7 divides 9227 by NAT_4:9; :: thesis:
9227 = (11 * 838) + 9 ;
hence not 11 divides 9227 by NAT_4:9; :: thesis:
9227 = (13 * 709) + 10 ;
hence not 13 divides 9227 by NAT_4:9; :: thesis:
9227 = (17 * 542) + 13 ;
hence not 17 divides 9227 by NAT_4:9; :: thesis:
9227 = (19 * 485) + 12 ;
hence not 19 divides 9227 by NAT_4:9; :: thesis:
9227 = (23 * 401) + 4 ;
hence not 23 divides 9227 by NAT_4:9; :: thesis:
9227 = (29 * 318) + 5 ;
hence not 29 divides 9227 by NAT_4:9; :: thesis:
9227 = (31 * 297) + 20 ;
hence not 31 divides 9227 by NAT_4:9; :: thesis:
9227 = (37 * 249) + 14 ;
hence not 37 divides 9227 by NAT_4:9; :: thesis:
9227 = (41 * 225) + 2 ;
hence not 41 divides 9227 by NAT_4:9; :: thesis:
9227 = (43 * 214) + 25 ;
hence not 43 divides 9227 by NAT_4:9; :: thesis:
9227 = (47 * 196) + 15 ;
hence not 47 divides 9227 by NAT_4:9; :: thesis:
9227 = (53 * 174) + 5 ;
hence not 53 divides 9227 by NAT_4:9; :: thesis:
9227 = (59 * 156) + 23 ;
hence not 59 divides 9227 by NAT_4:9; :: thesis:
9227 = (61 * 151) + 16 ;
hence not 61 divides 9227 by NAT_4:9; :: thesis:
9227 = (67 * 137) + 48 ;
hence not 67 divides 9227 by NAT_4:9; :: thesis:
9227 = (71 * 129) + 68 ;
hence not 71 divides 9227 by NAT_4:9; :: thesis:
9227 = (73 * 126) + 29 ;
hence not 73 divides 9227 by NAT_4:9; :: thesis:
9227 = (79 * 116) + 63 ;
hence not 79 divides 9227 by NAT_4:9; :: thesis:
9227 = (83 * 111) + 14 ;
hence not 83 divides 9227 by NAT_4:9; :: thesis:
9227 = (89 * 103) + 60 ;
hence not 89 divides 9227 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9227 & n is prime holds
not n divides 9227 by XPRIMET1:48;
hence 9227 is prime by NAT_4:14; :: thesis: