6329 = (2 * 3164) + 1 ;
hence not 2 divides 6329 by NAT_4:9; :: thesis:
6329 = (3 * 2109) + 2 ;
hence not 3 divides 6329 by NAT_4:9; :: thesis:
6329 = (5 * 1265) + 4 ;
hence not 5 divides 6329 by NAT_4:9; :: thesis:
6329 = (7 * 904) + 1 ;
hence not 7 divides 6329 by NAT_4:9; :: thesis:
6329 = (11 * 575) + 4 ;
hence not 11 divides 6329 by NAT_4:9; :: thesis:
6329 = (13 * 486) + 11 ;
hence not 13 divides 6329 by NAT_4:9; :: thesis:
6329 = (17 * 372) + 5 ;
hence not 17 divides 6329 by NAT_4:9; :: thesis:
6329 = (19 * 333) + 2 ;
hence not 19 divides 6329 by NAT_4:9; :: thesis:
6329 = (23 * 275) + 4 ;
hence not 23 divides 6329 by NAT_4:9; :: thesis:
6329 = (29 * 218) + 7 ;
hence not 29 divides 6329 by NAT_4:9; :: thesis:
6329 = (31 * 204) + 5 ;
hence not 31 divides 6329 by NAT_4:9; :: thesis:
6329 = (37 * 171) + 2 ;
hence not 37 divides 6329 by NAT_4:9; :: thesis:
6329 = (41 * 154) + 15 ;
hence not 41 divides 6329 by NAT_4:9; :: thesis:
6329 = (43 * 147) + 8 ;
hence not 43 divides 6329 by NAT_4:9; :: thesis:
6329 = (47 * 134) + 31 ;
hence not 47 divides 6329 by NAT_4:9; :: thesis:
6329 = (53 * 119) + 22 ;
hence not 53 divides 6329 by NAT_4:9; :: thesis:
6329 = (59 * 107) + 16 ;
hence not 59 divides 6329 by NAT_4:9; :: thesis:
6329 = (61 * 103) + 46 ;
hence not 61 divides 6329 by NAT_4:9; :: thesis:
6329 = (67 * 94) + 31 ;
hence not 67 divides 6329 by NAT_4:9; :: thesis:
6329 = (71 * 89) + 10 ;
hence not 71 divides 6329 by NAT_4:9; :: thesis:
6329 = (73 * 86) + 51 ;
hence not 73 divides 6329 by NAT_4:9; :: thesis:
6329 = (79 * 80) + 9 ;
hence not 79 divides 6329 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 6329 & n is prime holds
not n divides 6329 by XPRIMET1:44;
hence 6329 is prime by NAT_4:14; :: thesis: