Every one of those payments that you received were essentially worthless. The site that sent them to you probably knew they were sending you worthless amounts, but they didn't care. They were still getting their profits from advertising revenue. Effectively, you've been scammed.
They were not in 2013. The payments were coming till October last year or so. I managed to move some at lest in 2015.
It's not a big loss for me but having any money that is unspendable yet perfectly legit means the currency is broken. (And it looks like 0.0001BTC is not a "legal tender" any more which happened without any announcement).
It's 0.0001 today and might be 0.01 in a year (just depends on what miners will find profitable at that time). Just wonder what happens when there is no more new coins to dig. The commission will be the sole source of profit... unless the miners will hardfork bitcoin into an ever lasting source of new bitcoins or whatever. That means Bitcoin is broken beyond repair no matter how you will ridicule people with small coins (I remember the days of bitcoin faucet sending such coins for free).
p.s. yes, i mistyped one 0, the screenshots were correct though.
p.s.: This is the the address with the dust: https://blockchain.info/address/1AsPzC53491jKTvwrUEZnvF6cgtXDWD8mX... and I can tell there's more addresses with such small coins:
https://blockchain.info/related_tags?active=1AsPzC53491jKTvwrUEZnvF6cgtXDWD8mX
I remember when I was reading about bitcoin a dacade ago or so it was meant to be perfectly suited for micropayments... now it's turned into micro-pain-ments
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