9173 = (2 * 4586) + 1 ;
hence not 2 divides 9173 by NAT_4:9; :: thesis:
9173 = (3 * 3057) + 2 ;
hence not 3 divides 9173 by NAT_4:9; :: thesis:
9173 = (5 * 1834) + 3 ;
hence not 5 divides 9173 by NAT_4:9; :: thesis:
9173 = (7 * 1310) + 3 ;
hence not 7 divides 9173 by NAT_4:9; :: thesis:
9173 = (11 * 833) + 10 ;
hence not 11 divides 9173 by NAT_4:9; :: thesis:
9173 = (13 * 705) + 8 ;
hence not 13 divides 9173 by NAT_4:9; :: thesis:
9173 = (17 * 539) + 10 ;
hence not 17 divides 9173 by NAT_4:9; :: thesis:
9173 = (19 * 482) + 15 ;
hence not 19 divides 9173 by NAT_4:9; :: thesis:
9173 = (23 * 398) + 19 ;
hence not 23 divides 9173 by NAT_4:9; :: thesis:
9173 = (29 * 316) + 9 ;
hence not 29 divides 9173 by NAT_4:9; :: thesis:
9173 = (31 * 295) + 28 ;
hence not 31 divides 9173 by NAT_4:9; :: thesis:
9173 = (37 * 247) + 34 ;
hence not 37 divides 9173 by NAT_4:9; :: thesis:
9173 = (41 * 223) + 30 ;
hence not 41 divides 9173 by NAT_4:9; :: thesis:
9173 = (43 * 213) + 14 ;
hence not 43 divides 9173 by NAT_4:9; :: thesis:
9173 = (47 * 195) + 8 ;
hence not 47 divides 9173 by NAT_4:9; :: thesis:
9173 = (53 * 173) + 4 ;
hence not 53 divides 9173 by NAT_4:9; :: thesis:
9173 = (59 * 155) + 28 ;
hence not 59 divides 9173 by NAT_4:9; :: thesis:
9173 = (61 * 150) + 23 ;
hence not 61 divides 9173 by NAT_4:9; :: thesis:
9173 = (67 * 136) + 61 ;
hence not 67 divides 9173 by NAT_4:9; :: thesis:
9173 = (71 * 129) + 14 ;
hence not 71 divides 9173 by NAT_4:9; :: thesis:
9173 = (73 * 125) + 48 ;
hence not 73 divides 9173 by NAT_4:9; :: thesis:
9173 = (79 * 116) + 9 ;
hence not 79 divides 9173 by NAT_4:9; :: thesis:
9173 = (83 * 110) + 43 ;
hence not 83 divides 9173 by NAT_4:9; :: thesis:
9173 = (89 * 103) + 6 ;
hence not 89 divides 9173 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9173 & n is prime holds
not n divides 9173 by XPRIMET1:48;
hence 9173 is prime by NAT_4:14; :: thesis: