6449 = (2 * 3224) + 1 ;
hence not 2 divides 6449 by NAT_4:9; :: thesis:
6449 = (3 * 2149) + 2 ;
hence not 3 divides 6449 by NAT_4:9; :: thesis:
6449 = (5 * 1289) + 4 ;
hence not 5 divides 6449 by NAT_4:9; :: thesis:
6449 = (7 * 921) + 2 ;
hence not 7 divides 6449 by NAT_4:9; :: thesis:
6449 = (11 * 586) + 3 ;
hence not 11 divides 6449 by NAT_4:9; :: thesis:
6449 = (13 * 496) + 1 ;
hence not 13 divides 6449 by NAT_4:9; :: thesis:
6449 = (17 * 379) + 6 ;
hence not 17 divides 6449 by NAT_4:9; :: thesis:
6449 = (19 * 339) + 8 ;
hence not 19 divides 6449 by NAT_4:9; :: thesis:
6449 = (23 * 280) + 9 ;
hence not 23 divides 6449 by NAT_4:9; :: thesis:
6449 = (29 * 222) + 11 ;
hence not 29 divides 6449 by NAT_4:9; :: thesis:
6449 = (31 * 208) + 1 ;
hence not 31 divides 6449 by NAT_4:9; :: thesis:
6449 = (37 * 174) + 11 ;
hence not 37 divides 6449 by NAT_4:9; :: thesis:
6449 = (41 * 157) + 12 ;
hence not 41 divides 6449 by NAT_4:9; :: thesis:
6449 = (43 * 149) + 42 ;
hence not 43 divides 6449 by NAT_4:9; :: thesis:
6449 = (47 * 137) + 10 ;
hence not 47 divides 6449 by NAT_4:9; :: thesis:
6449 = (53 * 121) + 36 ;
hence not 53 divides 6449 by NAT_4:9; :: thesis:
6449 = (59 * 109) + 18 ;
hence not 59 divides 6449 by NAT_4:9; :: thesis:
6449 = (61 * 105) + 44 ;
hence not 61 divides 6449 by NAT_4:9; :: thesis:
6449 = (67 * 96) + 17 ;
hence not 67 divides 6449 by NAT_4:9; :: thesis:
6449 = (71 * 90) + 59 ;
hence not 71 divides 6449 by NAT_4:9; :: thesis:
6449 = (73 * 88) + 25 ;
hence not 73 divides 6449 by NAT_4:9; :: thesis:
6449 = (79 * 81) + 50 ;
hence not 79 divides 6449 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 6449 & n is prime holds
not n divides 6449 by XPRIMET1:44;
hence 6449 is prime by NAT_4:14; :: thesis: