9539 = (2 * 4769) + 1 ;
hence not 2 divides 9539 by NAT_4:9; :: thesis:
9539 = (3 * 3179) + 2 ;
hence not 3 divides 9539 by NAT_4:9; :: thesis:
9539 = (5 * 1907) + 4 ;
hence not 5 divides 9539 by NAT_4:9; :: thesis:
9539 = (7 * 1362) + 5 ;
hence not 7 divides 9539 by NAT_4:9; :: thesis:
9539 = (11 * 867) + 2 ;
hence not 11 divides 9539 by NAT_4:9; :: thesis:
9539 = (13 * 733) + 10 ;
hence not 13 divides 9539 by NAT_4:9; :: thesis:
9539 = (17 * 561) + 2 ;
hence not 17 divides 9539 by NAT_4:9; :: thesis:
9539 = (19 * 502) + 1 ;
hence not 19 divides 9539 by NAT_4:9; :: thesis:
9539 = (23 * 414) + 17 ;
hence not 23 divides 9539 by NAT_4:9; :: thesis:
9539 = (29 * 328) + 27 ;
hence not 29 divides 9539 by NAT_4:9; :: thesis:
9539 = (31 * 307) + 22 ;
hence not 31 divides 9539 by NAT_4:9; :: thesis:
9539 = (37 * 257) + 30 ;
hence not 37 divides 9539 by NAT_4:9; :: thesis:
9539 = (41 * 232) + 27 ;
hence not 41 divides 9539 by NAT_4:9; :: thesis:
9539 = (43 * 221) + 36 ;
hence not 43 divides 9539 by NAT_4:9; :: thesis:
9539 = (47 * 202) + 45 ;
hence not 47 divides 9539 by NAT_4:9; :: thesis:
9539 = (53 * 179) + 52 ;
hence not 53 divides 9539 by NAT_4:9; :: thesis:
9539 = (59 * 161) + 40 ;
hence not 59 divides 9539 by NAT_4:9; :: thesis:
9539 = (61 * 156) + 23 ;
hence not 61 divides 9539 by NAT_4:9; :: thesis:
9539 = (67 * 142) + 25 ;
hence not 67 divides 9539 by NAT_4:9; :: thesis:
9539 = (71 * 134) + 25 ;
hence not 71 divides 9539 by NAT_4:9; :: thesis:
9539 = (73 * 130) + 49 ;
hence not 73 divides 9539 by NAT_4:9; :: thesis:
9539 = (79 * 120) + 59 ;
hence not 79 divides 9539 by NAT_4:9; :: thesis:
9539 = (83 * 114) + 77 ;
hence not 83 divides 9539 by NAT_4:9; :: thesis:
9539 = (89 * 107) + 16 ;
hence not 89 divides 9539 by NAT_4:9; :: thesis:
9539 = (97 * 98) + 33 ;
hence not 97 divides 9539 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9539 & n is prime holds
not n divides 9539 by XPRIMET1:50;
hence 9539 is prime by NAT_4:14; :: thesis: