Bitcoin Private (BTCP) was launched to provide a fork that fixed perceived anonymity weaknesses in Bitcoin's blockchain, a similar motivation that created other privacy-focused projects like Monero and Grin. BTCP is unique in that it fork-merges Bitcoin with Zclassic in an attempt to achieve lower fees, faster transaction throughput, and heightened on-chain confidentiality than Bitcoin. As is common among Bitcoin forks, BTCP also claims to fulfill certain aspects of Satoshi's "vision" for the original Bitcoin codebase.
Importantly, Bitcoin Private is a merge-fork with Zclassic to implement zero-knowledge non-interactive arguments of knowledge (zk-SNARKs) in Bitcoin. A merge fork simply combines the UTXO sets of two chains into one, new chain. BTCP also implements larger block sizes (2 MB) and shorter block times (2.5 minutes). BTCP also values ASIC-resistant mining which motivated their choice to implement the Equihash proof-of-work algorithm instead of SHA256. All ZClassic and Bitcoin addresses are eligible to receive 1 BTCP for every ZCL and BTC held before the merge-fork. Bitcoin Private difficulty adjusts every block, instead of every two weeks like Bitcoin.