More efficient algorithm using issue search and the org:name filter

Current algorithm (for reference):

1. Get all repos for a user (handles pagination)
2. Get all orgs for a user
3. For each org, loop through all repos in that org (handles pagination)
4. For each repo, if the user can push to it, collect that repo
5. For each repo from both the user and the users orgs, get all pull requests, filter by open (handles pagination)
6. Finally, we have all open pull requests that the user can merge

Proposed algorithm

1. Get all repos for a user (handles pagination)
2. Get all orgs for a user
3. Perform an issue search using the repo:<reponame> filter. (And the type:pr is:open filters of course.) It's paginated by 100 results.
4. Perform an issue search using the apparently undocumented org:<orgname> filter. This filter appears to be cumulative i.e. org:phonegap org:nodejs returns the set of PRs for phonegap union nodejs, so we can search for all open PRs across all repos of all relevant organisations at once.
5. Manually parse out the repo from the html_url property: https://github.com/nodejs/io.js/pull/2093 as there is no repo field or link on the result object itself.
6. For each repo, if the user can push to it, collect that repo
7. Filter PRs from steps 3 and 4 using repos from step 6.
8. Done.

This is somewhat more complex and may only work with public repos, but it should decrease the number of requests needed.

Start with the current repository/org enumeration and pull-request retrieval entry points described in the issue, then review GitHub issue search with the repo:, org:, type:pr, and is:open filters. Check pagination, pull-request repository extraction from html_url, and push-permission filtering, while comparing request counts for public repositories.