8273 = (2 * 4136) + 1 ;
hence not 2 divides 8273 by NAT_4:9; :: thesis:
8273 = (3 * 2757) + 2 ;
hence not 3 divides 8273 by NAT_4:9; :: thesis:
8273 = (5 * 1654) + 3 ;
hence not 5 divides 8273 by NAT_4:9; :: thesis:
8273 = (7 * 1181) + 6 ;
hence not 7 divides 8273 by NAT_4:9; :: thesis:
8273 = (11 * 752) + 1 ;
hence not 11 divides 8273 by NAT_4:9; :: thesis:
8273 = (13 * 636) + 5 ;
hence not 13 divides 8273 by NAT_4:9; :: thesis:
8273 = (17 * 486) + 11 ;
hence not 17 divides 8273 by NAT_4:9; :: thesis:
8273 = (19 * 435) + 8 ;
hence not 19 divides 8273 by NAT_4:9; :: thesis:
8273 = (23 * 359) + 16 ;
hence not 23 divides 8273 by NAT_4:9; :: thesis:
8273 = (29 * 285) + 8 ;
hence not 29 divides 8273 by NAT_4:9; :: thesis:
8273 = (31 * 266) + 27 ;
hence not 31 divides 8273 by NAT_4:9; :: thesis:
8273 = (37 * 223) + 22 ;
hence not 37 divides 8273 by NAT_4:9; :: thesis:
8273 = (41 * 201) + 32 ;
hence not 41 divides 8273 by NAT_4:9; :: thesis:
8273 = (43 * 192) + 17 ;
hence not 43 divides 8273 by NAT_4:9; :: thesis:
8273 = (47 * 176) + 1 ;
hence not 47 divides 8273 by NAT_4:9; :: thesis:
8273 = (53 * 156) + 5 ;
hence not 53 divides 8273 by NAT_4:9; :: thesis:
8273 = (59 * 140) + 13 ;
hence not 59 divides 8273 by NAT_4:9; :: thesis:
8273 = (61 * 135) + 38 ;
hence not 61 divides 8273 by NAT_4:9; :: thesis:
8273 = (67 * 123) + 32 ;
hence not 67 divides 8273 by NAT_4:9; :: thesis:
8273 = (71 * 116) + 37 ;
hence not 71 divides 8273 by NAT_4:9; :: thesis:
8273 = (73 * 113) + 24 ;
hence not 73 divides 8273 by NAT_4:9; :: thesis:
8273 = (79 * 104) + 57 ;
hence not 79 divides 8273 by NAT_4:9; :: thesis:
8273 = (83 * 99) + 56 ;
hence not 83 divides 8273 by NAT_4:9; :: thesis:
8273 = (89 * 92) + 85 ;
hence not 89 divides 8273 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 8273 & n is prime holds
not n divides 8273 by XPRIMET1:48;
hence 8273 is prime by NAT_4:14; :: thesis: