Apache :: Trying To Rewrite URLs With Query Strings

I need htaccess file for one of my sites. I've searched everywhere, and I can't find a solution for my problem.

System Info:
Easy Apache v3.18.1
CentOS 6.3 (x86_64)

So I'm trying to redirect all URLs in a certain query range to a new website. i.e.,

mydomain.com/?p=35000
mydomain.com/?p=35001
mydomain.com/?p=35002
mydomain.com/?p=35003
etc.

all need to 301 redirect to myotherdomain.com

I don't need to append each query to the new domain. All the URLs simply need to redirect to the naked domain of the other site. So

mydomain.com/?p=35000 is not redirecting to myotherdomain.com/?p=35000

It is simply redirecting to myotherdomain.com

Also, I need to redirect the specific series ([35000-35999]) to the new domain. I want to redirect the www and the non-www URLs.

I've attempted to write the code myself, but when I upload the htaccess file, the URLs are not redirecting. I'm doing something wrong.

Here's what I've tried:

Code:

RewriteEngine on
RewriteCond %{HTTP_HOST} ^mydomain.com$ [OR]
RewriteCond %{HTTP_HOST} ^www.mydomain.com$
RewriteCond %{QUERY_STRING} ^p=([35000-35999]*)$
RewriteRule ^(.*)$ "http://myotherdomain.com/" [R=301,L]