Unless NONE of your web users EVER login or you run only one web site(!) ... you can't rely on an 'anonymous' entry in database ACLs to allow everyone in.
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If you have a web site that is used by anonymous users AND by people who may already be authenticated with domino you need to make sure that -Default- has the same access as anonymous.
If -Default- is set to 'no access', someone who's logged in to another site but isn't in the access control list for your site will get repeated prompts to login - since they aren't anonymous that setting doesn't apply to them.