9929 = (2 * 4964) + 1 ;
hence not 2 divides 9929 by NAT_4:9; :: thesis:
9929 = (3 * 3309) + 2 ;
hence not 3 divides 9929 by NAT_4:9; :: thesis:
9929 = (5 * 1985) + 4 ;
hence not 5 divides 9929 by NAT_4:9; :: thesis:
9929 = (7 * 1418) + 3 ;
hence not 7 divides 9929 by NAT_4:9; :: thesis:
9929 = (11 * 902) + 7 ;
hence not 11 divides 9929 by NAT_4:9; :: thesis:
9929 = (13 * 763) + 10 ;
hence not 13 divides 9929 by NAT_4:9; :: thesis:
9929 = (17 * 584) + 1 ;
hence not 17 divides 9929 by NAT_4:9; :: thesis:
9929 = (19 * 522) + 11 ;
hence not 19 divides 9929 by NAT_4:9; :: thesis:
9929 = (23 * 431) + 16 ;
hence not 23 divides 9929 by NAT_4:9; :: thesis:
9929 = (29 * 342) + 11 ;
hence not 29 divides 9929 by NAT_4:9; :: thesis:
9929 = (31 * 320) + 9 ;
hence not 31 divides 9929 by NAT_4:9; :: thesis:
9929 = (37 * 268) + 13 ;
hence not 37 divides 9929 by NAT_4:9; :: thesis:
9929 = (41 * 242) + 7 ;
hence not 41 divides 9929 by NAT_4:9; :: thesis:
9929 = (43 * 230) + 39 ;
hence not 43 divides 9929 by NAT_4:9; :: thesis:
9929 = (47 * 211) + 12 ;
hence not 47 divides 9929 by NAT_4:9; :: thesis:
9929 = (53 * 187) + 18 ;
hence not 53 divides 9929 by NAT_4:9; :: thesis:
9929 = (59 * 168) + 17 ;
hence not 59 divides 9929 by NAT_4:9; :: thesis:
9929 = (61 * 162) + 47 ;
hence not 61 divides 9929 by NAT_4:9; :: thesis:
9929 = (67 * 148) + 13 ;
hence not 67 divides 9929 by NAT_4:9; :: thesis:
9929 = (71 * 139) + 60 ;
hence not 71 divides 9929 by NAT_4:9; :: thesis:
9929 = (73 * 136) + 1 ;
hence not 73 divides 9929 by NAT_4:9; :: thesis:
9929 = (79 * 125) + 54 ;
hence not 79 divides 9929 by NAT_4:9; :: thesis:
9929 = (83 * 119) + 52 ;
hence not 83 divides 9929 by NAT_4:9; :: thesis:
9929 = (89 * 111) + 50 ;
hence not 89 divides 9929 by NAT_4:9; :: thesis:
9929 = (97 * 102) + 35 ;
hence not 97 divides 9929 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9929 & n is prime holds
not n divides 9929 by XPRIMET1:50;
hence 9929 is prime by NAT_4:14; :: thesis: