No. 3: Electrum (software wallet). Electrum is a popular, free storage option in the bitcoin community, and is one of the most, if not the most, well-respected desktop storage apps out there. It's been around since 2011 and is also available for mobile, though Apple (ticker: AAPL) iPhone users are out of luck – to date it's only supported by Android.
How do they find this number? By guessing at random. The hash function makes it impossible to predict what the output will be. So, miners guess the mystery number and apply the hash function to the combination of that guessed number and the data in the block. The resulting hash has to start with a pre-established number of zeroes. There's no way of knowing which number will work, because two consecutive integers will give wildly varying results. What's more, there may be several nonces that produce the desired result, or there may be none (in which case the miners keep trying, but with a different block configuration).