Something here just isn't adding up for me. You're saying that just 30 days ago you sent over $6,000 worth of bitcoins somewhere, but you can't remember where you sent it?
Assuming this is true. When was the last time you remember seeing any balance on your desktop computer?
That does seem to be what I'm saying - you might think someone can't be that stupid, *I* can't imagine I'm that stupid (and I know me!). Last time I had the balance on my desktop was probably about 30 days ago ... but closing my eyes and trying to visualise I don't have active memory of that (if I did I'd know what I did rather than just be guessing what I did). Last time before that I could confirm I absolutely had balance would likely be in 2012 or very early 2013.
It appears that, of the 40.603 BTC balance, you sent exactly 4 BTC to 171wBfYRt1btkd53wLbw3wvmRpx7HcSfM, and the remaining 36.603 to 12YFP8qdKg4xbWugXvcDAeenKUUkqAtNxm? Odd that you wouldn't split them a bit more evenly if you were sending them to exchanges. Any idea which exchange you might prefer to send the larger amount to?
How many exchanges do you use? It might just be easier to look at your transaction history at each exchange and see how much you sent to each and when. Wouldn't that answer your question?
The split to 36.603 and 4 does make sense to me. Because around that time I was thinking that it might be useful to play the market a little. Keeping most (36.603 I guess) saved and use a small amount (guessing the 4 BTC) to speculate with - putting them into an exchange and selling them when the market rose a bit more to get some 'hard currency' into my account and then waiting for the next crash to buy as much as I could.
As I haven't actually done any such speculating with the small amount (I cannot conceive that I have and have forgotten that too), or anything at all with the large amount is what puzzles me. I want there to be a dead end on those amounts - as that would make sense with what I can remember planning to do but not following through on. Of course that would also mean the BTC was likely lost in a deleted wallet - which I don't want.
As for exchanges, I've only used britcoin/intersango (June 2011 last used), bitmarket.eu (June 2011 last used). I have accounts on intersango, MTGox, and bitmarket.eu - the first two show balances of 0.00319 and 0.00000000 respectively. BitMarket doesn't let me log in saying 'Only members with outstanding Bitcoin balance can log in!' I think BitMarket went bye-bye end of 2012 so unlikely that I transferred BTC in 30 days ago. I wouldn't be surprised if I have accounts on other exchanges - just to have a look and see what they're like - none spring immediately to mind (form mind or history)
I have also speculated (desperately) that I might have used an online wallet and have gone to
https://blockchain.info/wallet and punched in the few email addresses I use into the forgotten password option in case I put them there (but again they'd just dead-end rather than show further transactions so that seems unlikely too!).