3257 = (2 * 1628) + 1 ;
hence not 2 divides 3257 by NAT_4:9; :: thesis:
3257 = (3 * 1085) + 2 ;
hence not 3 divides 3257 by NAT_4:9; :: thesis:
3257 = (5 * 651) + 2 ;
hence not 5 divides 3257 by NAT_4:9; :: thesis:
3257 = (7 * 465) + 2 ;
hence not 7 divides 3257 by NAT_4:9; :: thesis:
3257 = (11 * 296) + 1 ;
hence not 11 divides 3257 by NAT_4:9; :: thesis:
3257 = (13 * 250) + 7 ;
hence not 13 divides 3257 by NAT_4:9; :: thesis:
3257 = (17 * 191) + 10 ;
hence not 17 divides 3257 by NAT_4:9; :: thesis:
3257 = (19 * 171) + 8 ;
hence not 19 divides 3257 by NAT_4:9; :: thesis:
3257 = (23 * 141) + 14 ;
hence not 23 divides 3257 by NAT_4:9; :: thesis:
3257 = (29 * 112) + 9 ;
hence not 29 divides 3257 by NAT_4:9; :: thesis:
3257 = (31 * 105) + 2 ;
hence not 31 divides 3257 by NAT_4:9; :: thesis:
3257 = (37 * 88) + 1 ;
hence not 37 divides 3257 by NAT_4:9; :: thesis:
3257 = (41 * 79) + 18 ;
hence not 41 divides 3257 by NAT_4:9; :: thesis:
3257 = (43 * 75) + 32 ;
hence not 43 divides 3257 by NAT_4:9; :: thesis:
3257 = (47 * 69) + 14 ;
hence not 47 divides 3257 by NAT_4:9; :: thesis:
3257 = (53 * 61) + 24 ;
hence not 53 divides 3257 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3257 & n is prime holds
not n divides 3257 by XPRIMET1:32;
hence 3257 is prime by NAT_4:14; :: thesis: