This script reveals the pull requests which contain the unmerged commits between two branches.

find_pull_requests.sh

#!/usr/bin/env bash

url_prefix='https://github.com/USER_NAME/REPOSITORY_NAME/pull/'

src_branch='branch-a'
dest_branch='branch-b'

pull_requests=()

# 1. Find the commit hashes which are only included in dest_branch.
# 2. Search the pull requests which contain the commit hashes.
for commit_hash in $(git log --no-merges --right-only $src_branch..$dest_branch | grep -Eo ' [a-f0-9]+$')
do
  # Find only merge logs to reveal the pull request number
  pr=`git log --merges --oneline --reverse --ancestry-path $commit_hash...$dest_branch |
  grep 'Merge pull request #'                                                          |
  head -n 1                                                                            |
  cut -f5 -d ' '                                                                       |
  sed -e 's%#%%'`
  pull_requests+=($pr)
done

IFS=$'\n'
pull_requests=(`echo "${pull_requests[*]}" | sort | uniq`)
for item in ${pull_requests[@]}; do
  echo $url_prefix$item
done