I would encourage you to research Satoshi's exact quotes on this sort of thing. Your answer is correct, they wrote the code for Bitcoin before releasing the whitepaper. I am unsure about all of the times of release, and which hit public eye first; but at least from their perspective and words this is what happened :
I actually did this kind of backwards. I had to
write all the code before I could convince myself that I could solve every
problem, then I wrote the paper. I think I will be able to release the code
sooner than I could write a detailed spec. -Satoshi
I would suggest anyone to read some of their original e-mail threads
(most of my questions come from sources such as this) :
http://satoshi.nakamotoinstitute.org/emails/cryptography/1/It's funny that you worded it almost exactly the same as them, talking about solving problems, etc.
Thanks for that, bill! I did spend some time much earlier on reading up on lore... and was fortunate to have been around last year when even more new emails resurfaced in August. I know a lot of people prefer these to be left alone, but history is always important for simple posterity and the giving of context, especially to those who were (and still are) new to Bitcoin.
If only half the projects that launch now put half the effort Satoshi did into Bitcoin... the idea of having a working solution before the white paper hardly exists these days.
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Now that's how you answer a question! Good job buwaytress.
Thank you pugman!