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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
There are two that I know of:
YaCy: https://github.com/yacy/yacy_search_server (functional)
Seeks: https://github.com/beniz/seeks (defunct)
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There's also SearX, which isn't distributed but is a metasearch engine (pulls results from multiple search engines) that you can self-host.
https://github.com/searx/searx
NOTE:
The number of mentions on this list indicates mentions on common posts plus user suggested alternatives.
Hence, a higher number means a more popular project.