Momentum

2026-09-14T22:54:20Z

Apueblar: Base for Momentum explanation

'''Momentum''' is a [https://en.wikipedia.org/wiki/Memory-hard_function memory-hard function] [[proof of work]] algorithm proposed by Daniel Larimer. It is based on the [https://en.wikipedia.org/wiki/Birthday_problem birthday problem] and requires miners to use '''large amounts of memory''' while searching for a valid collision.

== Algorithm ==

Momentum uses a birthday-collision search. Given a hash of the block data, denoted as ''H'', miners generate a large number of candidate nonces and calculate a birthday hash for each candidate. The goal is to find two distinct nonces ''A'' and ''B'' such that:

<code>BirthdayHash(A + H) == BirthdayHash(B + H)</code>

The intermediate hash results are stored in memory, allowing collisions to be detected efficiently. The algorithm therefore makes the amount of available memory an important part of the mining process.

== Memory hardness ==

The main goal of Momentum is to '''make proof-of-work mining less suitable for specialized hardware such as application-specific integrated circuits (ASICs)'''. Instead of relying only on a large number of hash calculations, a miner must maintain a large table of intermediate results in memory.

Momentum was designed so that solutions could be generated using significant amounts of memory while still being relatively inexpensive to verify. The original proposal argued that this could reduce the advantage of highly specialized mining hardware.

However, the memory-hardness of a proof-of-work algorithm also depends on its [https://en.wikipedia.org/wiki/Space–time_tradeoff time-space tradeoff]. A sufficiently effective tradeoff can allow a miner to reduce memory requirements by performing additional computation, weakening the intended hardware resistance.

== Momentum effect ==

The name '''Momentum''' refers to a property of the search process. As a miner continues searching and its table of candidate hashes grows, the probability of finding a collision increases.

This gives miners an incentive to continue working with the same block data instead of repeatedly discarding their accumulated search state and starting again with a new block template.

== History ==

Momentum was proposed by Daniel Larimer, who described it as a family of memory-hard proof-of-work algorithms based on finding birthday collisions. The proposal was intended to address the increasing efficiency of specialized hardware for conventional proof-of-work algorithms.

Momentum was not adopted by Bitcoin as its proof-of-work algorithm. Bitcoin instead uses [[SHA-256]]-based [[proof of work]].

== Comparison with Equihash ==

Momentum and [[Equihash]] both use the '''generalized birthday problem''' as part of their construction. Equihash was introduced by Alex Biryukov and Dmitry Khovratovich as an asymmetric memory-hard proof-of-work with fast verification. Its design uses a generalized birthday problem and introduces mechanisms intended to make reducing memory more costly.

Equihash subsequently saw practical use in cryptocurrencies such as '''Zcash'''.

== See also ==

* [[Proof of work]]
* [[SHA-256]]
* [[Mining]]

== External links ==

* [http://www.hashcash.org/papers/momentum.pdf Momentum: A Memory-Hard Proof-of-Work via Finding Birthday Collisions] original paper by Daniel Larimer

[[Category:Mining]]
[[Category:Technical]]

Statistics

2026-09-06T22:07:39Z

Apueblar: Updated the values to current date (2026-07-09)

There are many places with good statistics about Bitcoin. For network stats, the best place to start is with your own [[full node]]. Following that, detailed information about addresses, mining, transaction volume, and adoption can be found on various sites tracking those metrics. Below is a summary of Bitcoin statistics as of December 2025.

== Supply & on-chain fundamentals ==

* '''Circulating supply''': ~20.08M BTC (95.6% of the 21M supply)
* '''Bitcoins left to mine''': ~919K BTC
* '''Estimated lost/ancient coins''': Reports suggest several million BTC (ancient supply accumulating over time, indicating a portion is likely inaccessible or lost)<ref>https://www.fidelitydigitalassets.com/research-and-insights/increasing-impact-bitcoins-ancient-supply</ref>
* '''Transaction volume''': Over 1.4 billion cumulative transactions<ref>https://www.blockchain.com/explorer/charts/n-transactions-total</ref>
* '''Addresses''': Over 100 million addresses<ref>https://bitcoinisdata.com/qtd_addr/</ref>, with roughly ~250 thousand new addresses per day<ref>https://bitcoinisdata.com/new_addr/</ref>

== Network health ==

* '''Reachable full nodes''': ~26,000+ reachable Bitcoin nodes<ref>https://bitnodes.io/</ref>
* '''SegWit adoption''': Around 92-98% of network transactions<ref>https://mainnet.observer/charts/transactions-spending-segwit/</ref>
* '''Taproot adoption''': Roughly ~3–10% of the network total, down from a 2024 peak above 40% that was driven largely by inscriptions (e.g., Ordinals)<ref>https://mainnet.observer/charts/transactions-spending-taproot/</ref>

== Mining ==

* '''Hash rate''': Over 0.98 zettahash/s global hash power<ref>https://bitinfocharts.com/comparison/bitcoin-hashrate.html#3y</ref>
* '''Fee subsidy''': Roughly ~99.3% of miner revenue comes from block rewards<ref>https://timechainstats.com/</ref>

== Broader adoption metrics ==

* '''Global cryptocurrency adoption''': Over 900,000 active Bitcoin users per day <ref>https://www.coingecko.com/research/publications/bitcoin-report-2025</ref>
* '''Spot Bitcoin ETF holdings''': Over ~1.40 BTC accumulated (~7.0% of total supply) since their launch in 2024<ref>https://bold.report/bitcoin/holdings</ref>
* '''Public company holdings''': Over 1M BTC held by publicly listed companies aggregated across firms (corporate treasuries accumulating BTC)
* '''Bitcoin legality''': Unrestricted in 132 out of 257 countries<ref>https://coin.dance/poli</ref>

== Websites with statistics ==

Here are some notable websites that can give you a quick overview of relevant statistics.

* [https://bitcoin.clarkmoody.com/dashboard/ Clark Moody Bitcoin Dashboard]
* [https://mainnet.observer/ mainnet-observer]
* [https://bitinfocharts.com/ BitInfoCharts]
* [https://timechainstats.com/ TimechainStats]
* [https://coin.dance/ Coin Dance]

== References ==

Bitcoin Wiki - User contributions [en]

Momentum

Statistics