If you don't want your pastes turning up in searches then you may want to just sign up for an account, which will allow you:
Free members can create unlimited 'public' pastes, 25 'unlisted' pastes, 10 'private' pastes.
If you need more than 10 private pastes, you can look into something like GitHub Gists which doesn't have a limit on how many you can create.
Gists don't count against the number of private repositories for an account. There's no limit on the number of gists that can be created by a user, including users with free accounts.
Also with GitHub Gists, if you initially created a public gist, but then later want to make it private, you can.
Keep in mind that by "private" they mean unlisted, where you just need the URL to access. But otherwise it will not be searchable.
Secret gists are the same as public gists, only they don't show up in Discover and they're not searchable. [...] Keep in mind that secret gists aren't private. If you send the URL of a secret gist to a friend, they'll be able to see it, which makes them great for quick collaboration. However, if someone you don't know discovers the URL, they'll also be able to see it.
You can embed private GitHub Gists like you can public ones.