3889 = (2 * 1944) + 1 ;
hence not 2 divides 3889 by NAT_4:9; :: thesis:
3889 = (3 * 1296) + 1 ;
hence not 3 divides 3889 by NAT_4:9; :: thesis:
3889 = (5 * 777) + 4 ;
hence not 5 divides 3889 by NAT_4:9; :: thesis:
3889 = (7 * 555) + 4 ;
hence not 7 divides 3889 by NAT_4:9; :: thesis:
3889 = (11 * 353) + 6 ;
hence not 11 divides 3889 by NAT_4:9; :: thesis:
3889 = (13 * 299) + 2 ;
hence not 13 divides 3889 by NAT_4:9; :: thesis:
3889 = (17 * 228) + 13 ;
hence not 17 divides 3889 by NAT_4:9; :: thesis:
3889 = (19 * 204) + 13 ;
hence not 19 divides 3889 by NAT_4:9; :: thesis:
3889 = (23 * 169) + 2 ;
hence not 23 divides 3889 by NAT_4:9; :: thesis:
3889 = (29 * 134) + 3 ;
hence not 29 divides 3889 by NAT_4:9; :: thesis:
3889 = (31 * 125) + 14 ;
hence not 31 divides 3889 by NAT_4:9; :: thesis:
3889 = (37 * 105) + 4 ;
hence not 37 divides 3889 by NAT_4:9; :: thesis:
3889 = (41 * 94) + 35 ;
hence not 41 divides 3889 by NAT_4:9; :: thesis:
3889 = (43 * 90) + 19 ;
hence not 43 divides 3889 by NAT_4:9; :: thesis:
3889 = (47 * 82) + 35 ;
hence not 47 divides 3889 by NAT_4:9; :: thesis:
3889 = (53 * 73) + 20 ;
hence not 53 divides 3889 by NAT_4:9; :: thesis:
3889 = (59 * 65) + 54 ;
hence not 59 divides 3889 by NAT_4:9; :: thesis:
3889 = (61 * 63) + 46 ;
hence not 61 divides 3889 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3889 & n is prime holds
not n divides 3889 by XPRIMET1:36;
hence 3889 is prime by NAT_4:14; :: thesis: