3271 = (2 * 1635) + 1 ;
hence not 2 divides 3271 by NAT_4:9; :: thesis:
3271 = (3 * 1090) + 1 ;
hence not 3 divides 3271 by NAT_4:9; :: thesis:
3271 = (5 * 654) + 1 ;
hence not 5 divides 3271 by NAT_4:9; :: thesis:
3271 = (7 * 467) + 2 ;
hence not 7 divides 3271 by NAT_4:9; :: thesis:
3271 = (11 * 297) + 4 ;
hence not 11 divides 3271 by NAT_4:9; :: thesis:
3271 = (13 * 251) + 8 ;
hence not 13 divides 3271 by NAT_4:9; :: thesis:
3271 = (17 * 192) + 7 ;
hence not 17 divides 3271 by NAT_4:9; :: thesis:
3271 = (19 * 172) + 3 ;
hence not 19 divides 3271 by NAT_4:9; :: thesis:
3271 = (23 * 142) + 5 ;
hence not 23 divides 3271 by NAT_4:9; :: thesis:
3271 = (29 * 112) + 23 ;
hence not 29 divides 3271 by NAT_4:9; :: thesis:
3271 = (31 * 105) + 16 ;
hence not 31 divides 3271 by NAT_4:9; :: thesis:
3271 = (37 * 88) + 15 ;
hence not 37 divides 3271 by NAT_4:9; :: thesis:
3271 = (41 * 79) + 32 ;
hence not 41 divides 3271 by NAT_4:9; :: thesis:
3271 = (43 * 76) + 3 ;
hence not 43 divides 3271 by NAT_4:9; :: thesis:
3271 = (47 * 69) + 28 ;
hence not 47 divides 3271 by NAT_4:9; :: thesis:
3271 = (53 * 61) + 38 ;
hence not 53 divides 3271 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3271 & n is prime holds
not n divides 3271 by XPRIMET1:32;
hence 3271 is prime by NAT_4:14; :: thesis: