6469 = (2 * 3234) + 1 ;
hence not 2 divides 6469 by NAT_4:9; :: thesis:
6469 = (3 * 2156) + 1 ;
hence not 3 divides 6469 by NAT_4:9; :: thesis:
6469 = (5 * 1293) + 4 ;
hence not 5 divides 6469 by NAT_4:9; :: thesis:
6469 = (7 * 924) + 1 ;
hence not 7 divides 6469 by NAT_4:9; :: thesis:
6469 = (11 * 588) + 1 ;
hence not 11 divides 6469 by NAT_4:9; :: thesis:
6469 = (13 * 497) + 8 ;
hence not 13 divides 6469 by NAT_4:9; :: thesis:
6469 = (17 * 380) + 9 ;
hence not 17 divides 6469 by NAT_4:9; :: thesis:
6469 = (19 * 340) + 9 ;
hence not 19 divides 6469 by NAT_4:9; :: thesis:
6469 = (23 * 281) + 6 ;
hence not 23 divides 6469 by NAT_4:9; :: thesis:
6469 = (29 * 223) + 2 ;
hence not 29 divides 6469 by NAT_4:9; :: thesis:
6469 = (31 * 208) + 21 ;
hence not 31 divides 6469 by NAT_4:9; :: thesis:
6469 = (37 * 174) + 31 ;
hence not 37 divides 6469 by NAT_4:9; :: thesis:
6469 = (41 * 157) + 32 ;
hence not 41 divides 6469 by NAT_4:9; :: thesis:
6469 = (43 * 150) + 19 ;
hence not 43 divides 6469 by NAT_4:9; :: thesis:
6469 = (47 * 137) + 30 ;
hence not 47 divides 6469 by NAT_4:9; :: thesis:
6469 = (53 * 122) + 3 ;
hence not 53 divides 6469 by NAT_4:9; :: thesis:
6469 = (59 * 109) + 38 ;
hence not 59 divides 6469 by NAT_4:9; :: thesis:
6469 = (61 * 106) + 3 ;
hence not 61 divides 6469 by NAT_4:9; :: thesis:
6469 = (67 * 96) + 37 ;
hence not 67 divides 6469 by NAT_4:9; :: thesis:
6469 = (71 * 91) + 8 ;
hence not 71 divides 6469 by NAT_4:9; :: thesis:
6469 = (73 * 88) + 45 ;
hence not 73 divides 6469 by NAT_4:9; :: thesis:
6469 = (79 * 81) + 70 ;
hence not 79 divides 6469 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 6469 & n is prime holds
not n divides 6469 by XPRIMET1:44;
hence 6469 is prime by NAT_4:14; :: thesis: