5449 = (2 * 2724) + 1 ;
hence not 2 divides 5449 by NAT_4:9; :: thesis:
5449 = (3 * 1816) + 1 ;
hence not 3 divides 5449 by NAT_4:9; :: thesis:
5449 = (5 * 1089) + 4 ;
hence not 5 divides 5449 by NAT_4:9; :: thesis:
5449 = (7 * 778) + 3 ;
hence not 7 divides 5449 by NAT_4:9; :: thesis:
5449 = (11 * 495) + 4 ;
hence not 11 divides 5449 by NAT_4:9; :: thesis:
5449 = (13 * 419) + 2 ;
hence not 13 divides 5449 by NAT_4:9; :: thesis:
5449 = (17 * 320) + 9 ;
hence not 17 divides 5449 by NAT_4:9; :: thesis:
5449 = (19 * 286) + 15 ;
hence not 19 divides 5449 by NAT_4:9; :: thesis:
5449 = (23 * 236) + 21 ;
hence not 23 divides 5449 by NAT_4:9; :: thesis:
5449 = (29 * 187) + 26 ;
hence not 29 divides 5449 by NAT_4:9; :: thesis:
5449 = (31 * 175) + 24 ;
hence not 31 divides 5449 by NAT_4:9; :: thesis:
5449 = (37 * 147) + 10 ;
hence not 37 divides 5449 by NAT_4:9; :: thesis:
5449 = (41 * 132) + 37 ;
hence not 41 divides 5449 by NAT_4:9; :: thesis:
5449 = (43 * 126) + 31 ;
hence not 43 divides 5449 by NAT_4:9; :: thesis:
5449 = (47 * 115) + 44 ;
hence not 47 divides 5449 by NAT_4:9; :: thesis:
5449 = (53 * 102) + 43 ;
hence not 53 divides 5449 by NAT_4:9; :: thesis:
5449 = (59 * 92) + 21 ;
hence not 59 divides 5449 by NAT_4:9; :: thesis:
5449 = (61 * 89) + 20 ;
hence not 61 divides 5449 by NAT_4:9; :: thesis:
5449 = (67 * 81) + 22 ;
hence not 67 divides 5449 by NAT_4:9; :: thesis:
5449 = (71 * 76) + 53 ;
hence not 71 divides 5449 by NAT_4:9; :: thesis:
5449 = (73 * 74) + 47 ;
hence not 73 divides 5449 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 5449 & n is prime holds
not n divides 5449 by XPRIMET1:42;
hence 5449 is prime by NAT_4:14; :: thesis: