6473 = (2 * 3236) + 1 ;
hence not 2 divides 6473 by NAT_4:9; :: thesis:
6473 = (3 * 2157) + 2 ;
hence not 3 divides 6473 by NAT_4:9; :: thesis:
6473 = (5 * 1294) + 3 ;
hence not 5 divides 6473 by NAT_4:9; :: thesis:
6473 = (7 * 924) + 5 ;
hence not 7 divides 6473 by NAT_4:9; :: thesis:
6473 = (11 * 588) + 5 ;
hence not 11 divides 6473 by NAT_4:9; :: thesis:
6473 = (13 * 497) + 12 ;
hence not 13 divides 6473 by NAT_4:9; :: thesis:
6473 = (17 * 380) + 13 ;
hence not 17 divides 6473 by NAT_4:9; :: thesis:
6473 = (19 * 340) + 13 ;
hence not 19 divides 6473 by NAT_4:9; :: thesis:
6473 = (23 * 281) + 10 ;
hence not 23 divides 6473 by NAT_4:9; :: thesis:
6473 = (29 * 223) + 6 ;
hence not 29 divides 6473 by NAT_4:9; :: thesis:
6473 = (31 * 208) + 25 ;
hence not 31 divides 6473 by NAT_4:9; :: thesis:
6473 = (37 * 174) + 35 ;
hence not 37 divides 6473 by NAT_4:9; :: thesis:
6473 = (41 * 157) + 36 ;
hence not 41 divides 6473 by NAT_4:9; :: thesis:
6473 = (43 * 150) + 23 ;
hence not 43 divides 6473 by NAT_4:9; :: thesis:
6473 = (47 * 137) + 34 ;
hence not 47 divides 6473 by NAT_4:9; :: thesis:
6473 = (53 * 122) + 7 ;
hence not 53 divides 6473 by NAT_4:9; :: thesis:
6473 = (59 * 109) + 42 ;
hence not 59 divides 6473 by NAT_4:9; :: thesis:
6473 = (61 * 106) + 7 ;
hence not 61 divides 6473 by NAT_4:9; :: thesis:
6473 = (67 * 96) + 41 ;
hence not 67 divides 6473 by NAT_4:9; :: thesis:
6473 = (71 * 91) + 12 ;
hence not 71 divides 6473 by NAT_4:9; :: thesis:
6473 = (73 * 88) + 49 ;
hence not 73 divides 6473 by NAT_4:9; :: thesis:
6473 = (79 * 81) + 74 ;
hence not 79 divides 6473 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 6473 & n is prime holds
not n divides 6473 by XPRIMET1:44;
hence 6473 is prime by NAT_4:14; :: thesis: