1471 = (2 * 735) + 1 ;
hence not 2 divides 1471 by NAT_4:9; :: thesis:
1471 = (3 * 490) + 1 ;
hence not 3 divides 1471 by NAT_4:9; :: thesis:
1471 = (5 * 294) + 1 ;
hence not 5 divides 1471 by NAT_4:9; :: thesis:
1471 = (7 * 210) + 1 ;
hence not 7 divides 1471 by NAT_4:9; :: thesis:
1471 = (11 * 133) + 8 ;
hence not 11 divides 1471 by NAT_4:9; :: thesis:
1471 = (13 * 113) + 2 ;
hence not 13 divides 1471 by NAT_4:9; :: thesis:
1471 = (17 * 86) + 9 ;
hence not 17 divides 1471 by NAT_4:9; :: thesis:
1471 = (19 * 77) + 8 ;
hence not 19 divides 1471 by NAT_4:9; :: thesis:
1471 = (23 * 63) + 22 ;
hence not 23 divides 1471 by NAT_4:9; :: thesis:
1471 = (29 * 50) + 21 ;
hence not 29 divides 1471 by NAT_4:9; :: thesis:
1471 = (31 * 47) + 14 ;
hence not 31 divides 1471 by NAT_4:9; :: thesis:
1471 = (37 * 39) + 28 ;
hence not 37 divides 1471 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 1471 & n is prime holds
not n divides 1471 by XPRIMET1:24;
hence 1471 is prime by NAT_4:14; :: thesis: