I had the idea of a P2P search engine. Its informal and I have no real plans to develop it (yet?), but I just wanted to share it and get opinions or ideas.
So the "search engine" would be miners/nodes on the network. There would be two jobs for the miners. They would need to crawl the web and produce the massive page rank array that is then used by the other miners to service search results. Miners would be paid in "coins", which could then be sold to users. The page rank array would be akin to the block chain, but it only evolve on a local level based on the miner crawling the web and adding to its part of the array.
So their is proof of work, namely crawling and adding to the web; there would have to be miners that "fight" the crawlers to verify that the crawlers are creating proper links otherwise the proof of would would easily be could by just submitting garbage data.
Also proof of work for the miners who search their local copy of the page rank table to produce search results for users, these would be correlated over the network (multiple "miners" would hold duplicate page rank data) to produce a final results with an "accuracy" rating based on which miners agree as to the results of the search.
There could also be proof of stake for "miners" who just hold part of the page rank array and "occasionally verify" with the network; they would hold "stronger" links in the web, basically pages that always link to each other and have for a long time. This would keep malicious miners from overtime slowly changing search results in their favor.
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Obviously that's a lot, not well thought out, missing logic, and I'm not sure if I understand proof of stake versus proof of work. But I just wanted to bring it up for discussion.