sql - Index on date field mysql -

i have table screenshot 3 fields:

create table `screenshot` (   `id` int(11) not null auto_increment,   `userid` int(11) not null,   `datetaken` date not null,   primary key (`id`),   key `datetaken` (`datetaken`),   key `userid` (`userid`) using btree,   constraint `userid_foreign_key` foreign key (`userid`) references `users` (`userid`) ) engine=innodb auto_increment=22514871 default charset=latin1 

and

select @@innodb_buffer_pool_size 

result: 16777216

query:

select count(id) total         screenshot datetaken between '2000-05-01' , '2000-06-10' 

result : 2828844

explain output:

id|select_type|   table  |type |possible_keys|   key   |key_len| rows  |extra 1 |  simple   |screenshot|range|  datetaken  |datetaken|  3    |5730138|using where; using index 

here problem: have added index datetaken column , yet scanning rows (explain output) bigger result. seems whole scan table. , query runtime query takes 15 seconds. how can improve speed in query above?

you try adding composite index

  create index test on screenshot (datetaken, id)