17449 = (2 * 8724) + 1 ;
hence not 2 divides 17449 by NAT_4:9; :: thesis:
17449 = (3 * 5816) + 1 ;
hence not 3 divides 17449 by NAT_4:9; :: thesis:
17449 = (5 * 3489) + 4 ;
hence not 5 divides 17449 by NAT_4:9; :: thesis:
17449 = (7 * 2492) + 5 ;
hence not 7 divides 17449 by NAT_4:9; :: thesis:
17449 = (11 * 1586) + 3 ;
hence not 11 divides 17449 by NAT_4:9; :: thesis:
17449 = (13 * 1342) + 3 ;
hence not 13 divides 17449 by NAT_4:9; :: thesis:
17449 = (17 * 1026) + 7 ;
hence not 17 divides 17449 by NAT_4:9; :: thesis:
17449 = (19 * 918) + 7 ;
hence not 19 divides 17449 by NAT_4:9; :: thesis:
17449 = (23 * 758) + 15 ;
hence not 23 divides 17449 by NAT_4:9; :: thesis:
17449 = (29 * 601) + 20 ;
hence not 29 divides 17449 by NAT_4:9; :: thesis:
17449 = (31 * 562) + 27 ;
hence not 31 divides 17449 by NAT_4:9; :: thesis:
17449 = (37 * 471) + 22 ;
hence not 37 divides 17449 by NAT_4:9; :: thesis:
17449 = (41 * 425) + 24 ;
hence not 41 divides 17449 by NAT_4:9; :: thesis:
17449 = (43 * 405) + 34 ;
hence not 43 divides 17449 by NAT_4:9; :: thesis:
17449 = (47 * 371) + 12 ;
hence not 47 divides 17449 by NAT_4:9; :: thesis:
17449 = (53 * 329) + 12 ;
hence not 53 divides 17449 by NAT_4:9; :: thesis:
17449 = (59 * 295) + 44 ;
hence not 59 divides 17449 by NAT_4:9; :: thesis:
17449 = (61 * 286) + 3 ;
hence not 61 divides 17449 by NAT_4:9; :: thesis:
17449 = (67 * 260) + 29 ;
hence not 67 divides 17449 by NAT_4:9; :: thesis:
17449 = (71 * 245) + 54 ;
hence not 71 divides 17449 by NAT_4:9; :: thesis:
17449 = (73 * 239) + 2 ;
hence not 73 divides 17449 by NAT_4:9; :: thesis:
17449 = (79 * 220) + 69 ;
hence not 79 divides 17449 by NAT_4:9; :: thesis:
17449 = (83 * 210) + 19 ;
hence not 83 divides 17449 by NAT_4:9; :: thesis:
17449 = (89 * 196) + 5 ;
hence not 89 divides 17449 by NAT_4:9; :: thesis:
17449 = (97 * 179) + 86 ;
hence not 97 divides 17449 by NAT_4:9; :: thesis:
17449 = (101 * 172) + 77 ;
hence not 101 divides 17449 by NAT_4:9; :: thesis:
17449 = (103 * 169) + 42 ;
hence not 103 divides 17449 by NAT_4:9; :: thesis:
17449 = (107 * 163) + 8 ;
hence not 107 divides 17449 by NAT_4:9; :: thesis:
17449 = (109 * 160) + 9 ;
hence not 109 divides 17449 by NAT_4:9; :: thesis:
17449 = (113 * 154) + 47 ;
hence not 113 divides 17449 by NAT_4:9; :: thesis:
17449 = (127 * 137) + 50 ;
hence not 127 divides 17449 by NAT_4:9; :: thesis:
17449 = (131 * 133) + 26 ;
hence not 131 divides 17449 by NAT_4:9; :: thesis:

end;

then for p being Element of NAT st 1 < p & p * p <= 17449 & p is prime holds
not p divides 17449 by XPRIMET1:64;
hence 17449 is prime by NAT_4:14; :: thesis: