bitcoin-statistics

Simple application for running analysis on the Bitcoin network over the bitcoind JSON RPC.

About

Run a statistical analysis of the Bitcoin blockchain to answer the following questions:

1. How often does the Bitcoin network see two consecutive blocks mined more than 2 hours apart?
2. How many times has the above happened so far in the history of Bitcoin?

Setup

In order to utilize this program, you will need to setup a TOML config file to connect to your bitcoind RPC endpoint. You can also utilize ENV variables prefixed with APP_. See the src/config.example.toml file for more details on fields to configure.

Note: If you are running Umbrel, it is best to forward 127.0.0.1:PORT to umbrel.local:8332. You can setup a temporary SSH forward using ssh -f -L 8000:127.0.0.1:8332 umbrel@umbrel.local sleep 1000;

Usage

Run statistical analysis on Bitcoin blocks

USAGE:
    bitcoin-statistics [OPTIONS] <SUBCOMMAND>

OPTIONS:
    -c, --config <CONFIG>
            Path to config file if applicable [default: src/config]

    -f, --full-population <FULL_POPULATION>
            Run the analysis on the full population Small hack as clap does not handle bools
            properly [default: true]

    -h, --help
            Print help information

    -m, --margin-error <MARGIN_ERROR>
            Margin of error for sampling [default: 0.05]

    -s, --std-deviation <STD_DEVIATION>
            Standard deviation for sampling [default: 0.5]

    -V, --version
            Print version information

    -z, --z-score <Z_SCORE>
            Z-Score for sampling [default: 1.96]

SUBCOMMANDS:
    block-time-drift    Run the drift time analysis using a drift time as unix seconds
    help                Print this message or the help of the given subcommand(s)

Once configuration to your local bitcoind RPC node is setup, you can simply run cargo run block-time-drift to run the default statistical analysis. You can output the results to a file normally, cargo run block-time-drift > output.txt

Process

I decided that because I run my own node, I can access the blockchain data directly. I chose to use Rust as that is a language I enjoy using. This could also (more easily) be done using Python.

Assumptions

We know that the Bitcoin network attempts to maintain mining of blocks ocurring within a 10-minute window. This would give us about 6 blocks per hour. Thus, as the Bitcoin protocol attempts to provide a fixed-time block mining, we can assume a Poisson distribution. This would provide us with the formula 1 / (λ x E ^ (-2 x λ)) where λ = 6. I used a few online sources to assist me with these calculations as math is not my fondest skill. Using this, we get the following expectations for probability of seeing two consecutive blocks being mined over 2 hours apart:

Every 27126 hours / 1130 days / 3 years.

---

Testing the Assumption

At the time of this writing, there are over 748k blocks which gives us a fairly large population size. I decided to take a random sampling of the data using the Cochran Formula to determine the sample size to compare against the assumptions. One caveat is the inherit reliability of the data as block timestamps are not 100% accurate. As they are miner provided, the rule is that they fall within a two-hour window of network adjusted time and are greater than the median of the past 11 blocks. See BIP-113.

Data

Analysis was conducted around 748438 BST (Bitcoin Standard Time or block height)

Using a sample population resulted in few to no results after several consecutive runs. This would seem to support the original assumption considering that we should see this once every 3 years and given Bitcoin's age, there should only be around 4 incidents in total.

Utilizing a z-score of 1.96
With a standard deviation of 0.5
Within a 5.00% error margin
Sampling 384 blocks from a population of 748443
+------------------------------------+-----------------------------------+-------------------------------+
| Block Times                                                                                            |
+------------------------------------+-----------------------------------+-------------------------------+
| Parent Block Hash                  | Child Block Hash                  | Mining Time                   |
+------------------------------------+-----------------------------------+-------------------------------+
| Occurrences: 0, Mean: 9.97 minutes, Standard Deviation: 12.37, Poisson Probability: 1 / 27932.35 hours |
+------------------------------------+-----------------------------------+-------------------------------+

Utilizing a z-score of 1.96
With a standard deviation of 0.5
Within a 5.00% error margin
Sampling 384 blocks from a population of 748443
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| Block Times                                                                                                                                       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| Parent Block Hash                                                | Child Block Hash                                                 | Mining Time |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000162219e073a3db1debe242c2b5721bb8df5611cc09b44e95a48e2a91 | 00000000a9924bf2e932c6ec429481b453703398aa1683aaa99be9c5740953e9 | 194 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| Occurrences: 1, Mean: 9.54 minutes, Standard Deviation: 13.4, Poisson Probability: 1 / 46000.89 hours                                             |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+

A second pass using a lower margin of error resulting in a larger sample size:

Utilizing a z-score of 1.96
With a standard deviation of 0.5
Within a 1.00% error margin
Sampling 9480 blocks from a population of 748444
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| Block Times                                                                                                                                       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| Parent Block Hash                                                | Child Block Hash                                                 | Mining Time |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000093936119142f0f653103e3775ee53144dbbff9b01c9a9064380a0171 | 00000000de6d334392a180078b3d0086284e3d5e375e7da3d303d6569ef56b73 | 392 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000af24991ed5c28707afdb95b33d6a52d6117704d3605ea4efd1abbaeb | 0000000087a9bbec99e23f6b67c4569dc168450668503eda977cbc118ea698eb | 230 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000006a9a61f62ab4af162ed30272930c2acfc1139d6666455e60569a0a5c | 00000000dd431bce4cf36326ee8b51a7136ebcf664976ba7087bf7d8f3ce0f5d | 224 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000de6d334392a180078b3d0086284e3d5e375e7da3d303d6569ef56b73 | 000000005b0065cbd1fe6199a14a62baa264c17d432610a18d59275020be2159 | 150 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000000000000000b975fedb1fe62e271bd20d1fa74d2fe28dcfac6f761f3 | 0000000000000000000b5d9bcbd38c64e5a39bf4073f7a94348c1336618957ae | 122 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| Occurrences: 5, Mean: 9.48 minutes, Standard Deviation: 11.34, Poisson Probability: 1 / 49369.62 hours                                            |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+

Here, we have a total of 5 incidents where consecutive blocks exceed 2-hour intervals. Block hash 00000000de6d334392a180078b3d0086284e3d5e375e7da3d303d6569ef56b73 mined on 2009-08-22 at height 21446 being the longest in this sampling clocking in at over 6.5 hours.

As a result, I added the option to run a statistical analysis using the entire population set. This of course, took far longer to complete but provided a full picture:

Using total population of 748472
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| Block Times                                                                                                                                       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| Parent Block Hash                                                | Child Block Hash                                                 | Mining Time |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f | 00000000839a8e6886ab5951d76f411475428afc90947ee320161bbf18eb6048 | 7719 m      |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a367d068c6c60eaf5ac48769098cf9b0124bcb91e27dbe388470e3fd | 00000000720e7a19e31ca6cc9d2364705b49590f0ede8b0356cb46a8e486ab8f | 1508 m      |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000fe14ebcd6219d3cbfbc6550430826d8686c06377b7ffc915a64f82cf | 000000006dba4d567bdd008f233f826a05a2b9195324af92a231fbc9273cf901 | 1506 m      |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000080f17a0c5a67f663a9bc9969eb37e81666d9321125f0e293656f8a37 | 00000000b3322c8c3ef7d2cf6da009a776e6a99ee65ec5a32f3f345712238473 | 1452 m      |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000038b8fb10f5e6a0ff451d4ef4ba871fbcb7eb925f3e59c394e37cffb0 | 0000000058fcbaf4726da493b9bdf47bc0be2b1f224f31e01341eeb576c8acd6 | 1229 m      |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000002cbfbd983a7363525739e00a58ac2716c6ae78b360371a86318f71e7 | 0000000035a425c8689d3ad26574c4699fd62afe20d8ab412f3c20999587e92c | 1003 m      |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000f5138a3ae063a99bbb7f8d1edb25471524201bc7624e9dbd408328b4 | 00000000bef2501f26e11064cb3bd349de002ff50aca520e15d6d3dffc5d7e2a | 785 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000392dcf4bd5d4d3ca5106a5f76a2bdc13c58a9b141cf93eaef6a88136 | 00000000f969669f7db3908ce4a1598e0b1ddf341d02017cfe48352665a9263b | 636 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000e03d031ae6d78de2cdccb344fb6cccc729ce6098d3302ba7bc379636 | 00000000f68eccb15fe31a0b7a316de6b07d718b1b04d30720a8368eab2f196f | 625 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000071350772f98f84babf35502b33d42ee8466d3dde0f376c4120352081 | 00000000bb0d9430d3d1bab474be5050342161efcca9f7e45b151bff9a700944 | 514 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000b6928bb80f26b9937497b5932590be2840f3d78e3714b383e95fb61d | 00000000c4168c26f904f31a316a5bacf951c71c77eefb0aa12b84fbaa0f284a | 511 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000057756d646e8bf975bdb81c66658e269d714e8fef608cde216ca6bbbf | 00000000544380bd9b3610d75bfddf071a8ec2b23c2fd43372fec1ef5c48be73 | 507 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000001fccbc276846ef8e6f2592282dd6c11d0b097852693b961e127825d5 | 00000000dd23fc58d372dfde4f029e3ffeb538899978a9be6bca63f696ee51db | 500 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000000f5e08031af59b262769481370b26dedfd38c24b27e39167c009846e | 00000000cc596cf48d3748cac4a09fd7f2fa3765a808de46441327e7b96b62db | 488 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000052e73d8518a2d01958965c6990ce695837c8730e581b52881ee8c51e | 0000000075836a4523f3f3ce7e7b6ebf4187586d1f161e68ccb4ee4f3cff3e17 | 468 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000002dac70356f9d541597604a4347956204e3c6ae99737362eda6f6dcb7 | 00000000a722d4c9eeefb6ddf6933a585254fff8554603dea4850b75494d0580 | 433 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000007d3e674d6d827996e5d31e36b5995cc14f5a5ed4562adc5ef4175fa1 | 00000000a5f02b494d57da70f62350156d1bf1075b387e83d0bca1628dfb0efb | 422 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000181975d74adfa548eee6f36d7db15698711491f017281a237f85a28a | 00000000be4fc9af78c7265b7dc9b42d797d76282da494f4ed07e4031283eaa6 | 415 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000000606865e679308edf079991764d88e8122ca9250aef5386962b6e84 | 000000000069e1affe7161ab4bcbeacebb4ddf155b50e807f42de971b688a09b | 411 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000093936119142f0f653103e3775ee53144dbbff9b01c9a9064380a0171 | 00000000de6d334392a180078b3d0086284e3d5e375e7da3d303d6569ef56b73 | 392 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000062d93e6843e5be211c104c83bbb73567e37f6505adf5ddda8118eeff | 00000000ac06bc16068ab6971b3e43c5d62fd03b3d1022c7835e1711d56463ca | 384 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000008fe5d6a54317f32f1813755b597c715c1f3d24713b5beb5a1a47a44b | 00000000e17cb3ead21cbc0a6dafc3a6cacc4625645a5953fae3a10a277bc07e | 384 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000eaadf94b1d588bfff6173595c51c378c4fb9c183505b307d9ddae5c1 | 0000000001a039fa5e910ea377b598fe5b92f71caf09a30d447c8ff344cd6041 | 380 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000cb2f5853627c60e339388998e0f4fc71194e6186aedfe1b0ce1ca34f | 0000000072baa25f5b688b9c71fcfd695e045ab2c28106e322292f0ee10efd6c | 368 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000007c21e217c0d5aaeb4c9e7845a514e62c7165357a424430e70891c23b | 00000000e77778a088c48018de670e3e322e2e3f3f20d8d49c63749cced92870 | 357 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000002f53cae81cd5a5d48bb09c3a1bb9513964eadcd2a987a96663f2e2d6 | 000000003ce6abb8978fd84f8746f37bd47c327dae2c372f75627e052fedecc4 | 342 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000407f24682ba062854b2fcf11fe7978b38268dd09acfb0d3ec54dcf5e | 000000005bc3a591f4fb1eb824263897fc5b443a49770fe3f6e8ded565820a99 | 330 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000980f1a8fab4faa2c49c0a8f0ae4f7977e80708b7fd03266055b9f2be | 00000000aee2cabaf6c3c652e4936b43f9f60e5c5f591cb289818cabb74c3350 | 327 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000002218a47fc3cd49f16a2526e2a4c5949055efda451d3af46cf72d1958 | 0000000041a83b18f8f3cf1df306f681098b708f2df2b4b76df09f1562a37284 | 321 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000aee2cabaf6c3c652e4936b43f9f60e5c5f591cb289818cabb74c3350 | 00000000c4cb881455230762403a84d1a613e64d2c2319a3135683cbbc477818 | 308 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000018e2ea36c108d519eeed46c065b80355b2337fc60868c0f1d2458180 | 00000000a0dbe1086bbc9a9f4689d8aa25b91b4d2a575eb82dbd741e65561c48 | 305 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a7598111d0595321d2399d2b6f02ae7e61d1db8f46e45de6292c0481 | 000000007cafbd38e09d7812224cd55ec53394bdb50268bc0f62a69a527ca1bd | 302 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000018ee7999926286bacfac06e2850456adeb24108edd9364305e34da9f | 00000000ebe096e6677cbd27cd2e65065faa734e8203be3ba6fca83986138ff7 | 300 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000004b0a7e5dae713e8707163736e0072146bee3084ac7e16d54ffe38d62 | 000000007d181f33f2923502705b7a4cb2ec3c256e99ae1ef5ef5cb87748f381 | 299 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000008822a23fd8b7686f532d5c789d068704b380d0b415082b5b6dca6e81 | 00000000af7f8652ec21fc32c5e85ca52a3e2c56b1e7edefb8e8cef96dd0fbc3 | 294 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000cc81b1f9f5e1c5a5ba26847ee57959c21ddb341e3346a3b77af40edb | 000000001c3346ae3c598eceda97e992eb5211fadea1251c99f04c5c8b22675f | 285 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000c8c4533ed6a6d579c5b5e6280dd3d6ea3cc627aadc4d2996caa2358a | 0000000018ee7999926286bacfac06e2850456adeb24108edd9364305e34da9f | 277 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a32c685aaa574574bf40cccf8e44bb0dee3bc564c3d022b70513b710 | 00000000c87ed8d34a1797bb24e5090ebe69d6c0c8e3661f6908b3b7970f5931 | 263 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000013a10d0e05ebc7c24d0e82f9d7e7591a4bf57281c778125f5bcfcaff | 00000000921858b20e69ee3c0ed6d1419a02f17e253332009beb4a3bdfe3e77b | 263 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000005bc3a591f4fb1eb824263897fc5b443a49770fe3f6e8ded565820a99 | 00000000c8b2cb3a806f4814b1f2199de70a1cbf4c6250b517993f36ccc8b611 | 261 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000edff20adb2d7bb1308a4cc1ad5f0479c949df3b5159582b00196d93d | 000000006ed32719e6c6c4d6fde8cb97f46c5164ead2e561e608f59bef653070 | 260 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000005993ab9515911f072057bfa94b82cfa4e19ce072da2f6c2cc7d5269e | 0000000058f6ed42ea06ccc805d0b4ef361f02253e468be23a58d796f5ac4a62 | 259 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000e5d33e73b2cef6ecdf2b2e1f0e4b21e3c50bcb6febd2058717e95cfb | 00000000c76185ae8b09d2ea0c431708082167d613219e1ed4a48e768266b0ac | 248 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000009e495631ed3798ce861b50dfad193651c7b4810571b6b99f7e466bfd | 00000000a2d5a2ac3f6b1fa2be8e61545961c00ee40cb58c3a3e941f01b2508f | 237 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000e0a3a48835992a12f785a786b21c33d179121ff0cdcc6d8a6f679bec | 00000000a2bed8eb774caed69b9c37e9a725cec85ed8de73f430d3e296a72983 | 234 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000bef2501f26e11064cb3bd349de002ff50aca520e15d6d3dffc5d7e2a | 00000000181975d74adfa548eee6f36d7db15698711491f017281a237f85a28a | 234 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000015b9581a9292e69418ae3c0acf37866e3775067bc149e11cbb2b54df | 0000000078d5796955554bd1233f3210605751c5b6f902e886876a03bae05334 | 232 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000af24991ed5c28707afdb95b33d6a52d6117704d3605ea4efd1abbaeb | 0000000087a9bbec99e23f6b67c4569dc168450668503eda977cbc118ea698eb | 230 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000004b4f144a62698025cd0a2f4cd4a77e301c6482f860453fcae7451b28 | 00000000c76e8dc3887bfd38256ec9e40fa8b572fe261151d2abafcb34d79c3d | 226 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000004107e5dbc7d999c7496e4407c9b7d8daa6226e1035366026bcaff60d | 00000000e980a2637a3eb04fb53cefa7fbb804ae0d520a55b0edea172ab2d3e7 | 225 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000436617dc52052d5d5fbd8bf33f7693d1b66f56995889bc25755e813c | 000000002728faa7a41c17cb8c6364a059959292ab8bb8353382e770322f0e80 | 225 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000006a9a61f62ab4af162ed30272930c2acfc1139d6666455e60569a0a5c | 00000000dd431bce4cf36326ee8b51a7136ebcf664976ba7087bf7d8f3ce0f5d | 224 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000007a75787c2a4ea3811064628f1fbc774e75233bfa457e88c842aee030 | 0000000078d2d3825e6f12f22009d615954b3f59e42a29a18e922a374080021f | 223 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000567e95797f93675ac23683ae3787b183bb36859c18d9220f3fa66a69 | 000000002a22cfee1f2c846adbd12b3e183d4f97683f85dad08a79780a84bd55 | 222 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a95c3dfac37669ee6f653a9ca5a8620e9be8c49c554452a50725423f | 00000000407f24682ba062854b2fcf11fe7978b38268dd09acfb0d3ec54dcf5e | 220 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000f549ea89e2c7558b7f4032fd7c90da417b65acec6cbfd4942847b931 | 00000000bc6f96def17d3fd0532c7a33ad6efb746cd7f142226f6a11341d9c14 | 217 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000009add40fb84aaba2fdf36f2da161822be09c740eecbdce4bb0134f312 | 000000007c60db323d92f18fd267f76be0e251ae26305c62fc2c2409465fb44e | 217 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000b099c3d6044459c3d4673f3e3d7cd279c8ecc0f7f1696a8b0ac0274c | 0000000021dbcb6ce0f0ddd8eaa1f9a72b4fce141bfc05d72cff60820174f792 | 216 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000ace02fba9eb2b25bd11b8c632343111cdac17b25071557b5c788cb47 | 0000000081ac433c596a735022c5e1f19afcce061a68da4e8547521f647e5ca4 | 214 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000e7050ca0479ee3a47bc5b028bba56d4a1bed2e52e9317cd1fd633c08 | 00000000a8df21790d4785b6b2b9625f452ded9a3cec75b3160377aba5edceeb | 211 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000199ddfb75856a000afa29279e1fc6d438d853ad5baeb1b1d012bf861 | 000000005900fd3ea9d2798d73c82fb994f15ca4819569ffa8bd1ec23a8f002f | 211 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000072e767e1ccf2b1ac0c2ec016b97878238dd21a61e1625efcc311a527 | 0000000096c542c509e47b78b25d4d3a46c837e8b30011c65f0c2d7c547c484b | 208 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000096c758ad0d319df48048963d9026d7aaf24ec7c08a03fa1c612831c7 | 00000000b4ec7a38d98af46f6c853a6c2147376453bd29e25034403a9fdcd833 | 208 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000035a425c8689d3ad26574c4699fd62afe20d8ab412f3c20999587e92c | 0000000050e67c08b11edeaa9439fe1e78c7f4145e9ff13be9d0a466fa56aeb8 | 205 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000005b2ff6e5fe6a8a680374dd7e8120a130d22d2fd0e6ecc8d6352359d9 | 00000000be905c88edb210f918bfc7e214a9edbe9791318e6654a44481c7a399 | 202 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000003cb869ec8f67e0e4149d1bbfd376b4d24e428e435f54d261d3a5259f | 00000000ae564844cce06d19b23d24cc00cf6ba259761de0b4a107cd0957fbc9 | 198 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000800cca5d11742408e3965a84424269df7cecca5896649b1521d22297 | 00000000272568d8ad613b7f441fef896b912d21bca7ad2e18348e8b0ce483e7 | 196 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a2c925f08867154c4f171de18f65e0c17cdb8a461b892e27d0007ccc | 00000000ad66cc0d6f4381a74fe99dac4efebe51985857deabd75c2411aca232 | 196 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000294beac80a50b8faea71bb79612f7a3cf75f3e40b8606262b7c04309 | 0000000011b8654b41136e6314c70b770460a590437239fc170ff8b53d2e4181 | 196 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000162219e073a3db1debe242c2b5721bb8df5611cc09b44e95a48e2a91 | 00000000a9924bf2e932c6ec429481b453703398aa1683aaa99be9c5740953e9 | 194 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000afb05cd3dd91f99b3b2949377fdb6d72f0206ec1e93c25a040559f4b | 0000000069b4f643a24c41045ccefb29f40a73c45c94830c00b3994fe368bef3 | 194 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000046eb0934a822509c1011630427ee707f15d95bad7311d789da05a69b | 0000000079a1b2b4a500b9f5960cc940977a337111838df264bfe26a0e8057b0 | 191 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000009107a805852bc47a728d3c4e66e0563feee4460f9874d638d95361d7 | 00000000ea57beb87fa040cfbc88ac2631d0bbbd6a6b01621bdc00403854c2d8 | 190 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000089ad3ca8b464c87f920fa3346bf97c6961e299aeb9722348ef29a944 | 000000006440d96e5a77a85b27f99ab99dca1b4ba00d17c6a10139a3ea72f871 | 190 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000086410b1e0521711c177bd8975ce0f6f4fb06dd7d2eeb0bfffb2dbbf7 | 00000000d14ed5bff1d83c8fadccbdb206de78167a4c477330ca4da1e50ac6f2 | 190 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000046d234a513bcba7c73d6c9c2b2b43dace9033838b3eead334a7d39c1 | 000000009a4aed3e8ba7a978c6b50fea886fb496d66e696090a91d527200b002 | 188 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000ca3baba0bcfc7c078a312f067d0ebbf4e47d674bdbb2ebc823a76f51 | 0000000014757bd8dd519586dd54e9071b15914f5396a25cd6fd25218eb67658 | 188 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000039e74a999746a6296171022df8aab06347a37fb0a03712c272edc22f | 00000000d0104e311fbd578643e04d33668d6b25a56edd594705742f949c0d95 | 186 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a7215edeb27c7b2c8e75326977a6491254d2427243bf6f76350c4ab1 | 000000009340670d484a6af146dd43df703870a50ebead687ef249a53ff33f65 | 186 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a52d50acf0448afbd2b9bbeab486282a28d0355f2fc3e52c1353622b | 00000000b6e560049fb607dac3b5fc12cdfbbc38f3da35936770e47df9617383 | 186 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000907d21f4d0baf7c90da1550b8623cd0f700928cb14cbab386e807de7 | 00000000d93ac9f4ef41e2bfe57e8b2583a5197b6e1ee2035c671fe107fc00e5 | 179 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a2d5a2ac3f6b1fa2be8e61545961c00ee40cb58c3a3e941f01b2508f | 00000000ce32ae9ff346eacd74b753e7d44443c88a94b0aaeb3fc5db85a102ef | 178 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000006230c59ade37892bb71b40294f367c05f9b1407570ca047ad0b4aef0 | 00000000d5e5ab4d710ee96bb44eb0adc97b5eb643d3e7977980ba1cce1d6607 | 175 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000003496ef9e8c7b7ab66b512cc4841807902372238921bd247c65538703 | 000000001d0998f0ebe37d8518d71098603e3897bc2b69d7ca75dcb380af405b | 175 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000afe93193ee864e5efd7b09cb9e221f9e5f069509d8d858fd006936ef | 0000000066fd802a02909e8918fb85943836ce5d99000bdcd8128a06070d140a | 174 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000bedfbb268d32e50b36ac4d6d5ba70b6912128c592b810321ebff97b3 | 0000000032c349b31a64a7cd8cfae3287f2238db0ee82862f31256abdb575da2 | 174 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000007575baba90d9c0a0e269634d63b4959db6259e800bc5f2d1dab540d1 | 0000000033f711f7a56402334a33eec9acb5c5097502fbb1f3399dfa72759605 | 172 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000fae9ed331749a6191f4fedb3a84228d0eedc6e338ff89855fc1230f9 | 00000000acb681b7b6cc53456bda7e572578a7c8100128184ea0e249fe110157 | 170 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000d578beca7de110c13c5a0ca1ddb453f152cd05f993737b2b9ccc5782 | 000000006230c59ade37892bb71b40294f367c05f9b1407570ca047ad0b4aef0 | 170 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a00ad88fb12f0708a333c61fa8cc109986331d540290377e2577f02c | 000000006f20637d8d820bcadc9e062d7e5c3e98047b808a85d55a90ee85eb14 | 166 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a2886c95400fd3b263b9920af80b118b28fee5d2a162a18e4d9d8b2f | 0000000086e318e8c348dad73199bb6fac8cc1effb9c872a7dda49c5caca0021 | 165 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000006ff016a450230e2275c79e109751cb4a6efb02071d2c9cc1aafb6641 | 00000000cf85342951613ebbe9abd018124026908f1221aca60d34124759141b | 163 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000008072f0a4c913de39a45544fbd85ea91ade18bb541de3b77b868ba8cd | 00000000a25cd202aaf0b8674412e62d75bde46fd94d96a72183b9333fe1a004 | 162 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a8389cc6eeafb076599fabd8d2d7fa29c29e8f44661f95ab04c3396d | 00000000d85f2e814b555bafaf774a15da7df781f5ca9a1dc9e24c80009551bc | 162 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000639baedbb01ae10303705bbb321f5cf687174045934e65dd6995971d | 00000000a7598111d0595321d2399d2b6f02ae7e61d1db8f46e45de6292c0481 | 161 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000021dbcb6ce0f0ddd8eaa1f9a72b4fce141bfc05d72cff60820174f792 | 00000000aa483b338c6ff91a49dadc1fbf4587f2920bc58bb4b984c150c0fb7b | 161 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000051effd28b0f2c4ec54f1eacba4e72a65affced37ba7ef5da61d36a4d | 00000000817d6b8865386209d553767c74b1df8cec22750acaf87d25d2834c2d | 160 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000099af07d315b13f4ec0817583e5c2c0f899c8de3c11c7c500372b72df | 000000009d21f5616451b607e5b38bde7a816c7fca51acd031b5643c79ad6242 | 160 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000f8c87d19953100892af0a1d54e2c32aec6493abc5b8ddeb326f4b330 | 00000000600620ec54a2a2d640bf1a46fe50eb644a4e1e477aa274d93070c03b | 158 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a46605c6bfc7ac085f85c4d2c5f7688bd589e6c947c9ba8c374c79e4 | 0000000099af07d315b13f4ec0817583e5c2c0f899c8de3c11c7c500372b72df | 157 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a29e26a773bb74bdf522b518b59ef810f02938f20bbbc0fca6d27e42 | 00000000a853c360b4b3919386630d296fbaf497c386476a8d2857c0c3de7df0 | 157 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000b3114e7f6e56c6a9806526630303e4c3ede7adf6f2de6029911694ca | 000000006874937bd9cdb78069ad9967e5c2f6797700aac07fb6d7a030e21617 | 156 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000739c5e05d27949d20a623f246760e1006c9e6f29ca39c3ceba5a416f | 00000000800cca5d11742408e3965a84424269df7cecca5896649b1521d22297 | 155 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000921858b20e69ee3c0ed6d1419a02f17e253332009beb4a3bdfe3e77b | 00000000af24991ed5c28707afdb95b33d6a52d6117704d3605ea4efd1abbaeb | 155 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000cf02ee68fe5e52bf6579d35e25b89b715544e01ebb2af52f6e573a37 | 000000007af40ab6afe6d09436815a275db06dfe3c26e4d297fda0d9f24f8790 | 154 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000006783ca92b11bb5c370a3d500dfc19cb7f81b241ebb07a024316585c4 | 000000000ddadfebdf445b0d7b44621e98d6bafc91e0a7948bdc0f5454bf22f7 | 154 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000004a6375d83bb252d5458aecdafde944f432bfcbf5a91fe604b8160cca | 00000000e7d7fa57b59184cc635db8a1e96738ecd110ac54e5d422e954f225b0 | 153 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000de6d334392a180078b3d0086284e3d5e375e7da3d303d6569ef56b73 | 000000005b0065cbd1fe6199a14a62baa264c17d432610a18d59275020be2159 | 150 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000008ae57a20465ac4b4b4d08102089ca747796dcd195193ad3e77dea43d | 00000000a11cfd6425e1af804e3ca56ded2b521fe10b779121fc19d5cf37db6e | 150 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a25cd202aaf0b8674412e62d75bde46fd94d96a72183b9333fe1a004 | 00000000de536100e686e9039b0642e1598c84d915895c6f17b8d1a86cb46a38 | 148 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000010c4ae0c8edf9efc9fd38df2ec325f725a62969410d75884da0e98d6 | 00000000edc080d64924b0f5f5f099d98273914545753f4da9747c50d8fd4fe4 | 147 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000007929b947c796e589df436ba1976300341c50df4880dcc9f54406540c | 00000000957dd4b3a8977edd40768a2757e040fa0d79b7eeed6b92bac2b1ab42 | 146 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000b0aa1df23410bd69eadf201c6aa19e4544f4f0277b9f3cf1270e0497 | 00000000255a14c61ec1664de04580b1b05e06f3b17d9efab0b3f92d2eb6df83 | 146 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000e980a2637a3eb04fb53cefa7fbb804ae0d520a55b0edea172ab2d3e7 | 0000000013a10d0e05ebc7c24d0e82f9d7e7591a4bf57281c778125f5bcfcaff | 146 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000007c60db323d92f18fd267f76be0e251ae26305c62fc2c2409465fb44e | 000000008c6601fb72f860b32fc7cf747d402fd26e141b52a4188e0491957bbf | 146 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000089378befe73325952b17b8ec79d3c4f177fc060ce588fedf94e5c410 | 000000001c871b513815f9c1752301d2f4f8a558cbe733f60127516b91364c80 | 145 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000000000840048f55ccacc74b10bace1ea061a994cd8b5b48d07c8e841f | 000000000000092a5d77f0f3a2bf015a5198fff0bdf3d3fb600651874e7263e0 | 144 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000f65ec02ed1afe14a10abb94e08ca830ea8c5e47a8207f5e98d7fae65 | 000000006a9a61f62ab4af162ed30272930c2acfc1139d6666455e60569a0a5c | 143 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000000000036289b546359f1a7ae4d643ed0282c8866ba1c656a9122a8a1f | 00000000000004f6a74c54c7df842134e3f7a363c1a56137a63c3a2d1e869972 | 141 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000000000000000299c379f7a900bf937fcea9bab1ea55bd959e68266799 | 0000000000000000000ae9eca52d8f314f32fb5ac314d7bb18eb9e9c0f89326c | 139 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000009889527224695ca3201094f6c8324e8a18c292b2e3736e9c880543e8 | 0000000030e64de4829232019f9f05f98b203a1230ac4049a4436360ef3a6f99 | 139 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000549ce6eae52cbe10c12e53281ba6f1cb8b3c5780ec4ce466725ae89a | 000000009107a805852bc47a728d3c4e66e0563feee4460f9874d638d95361d7 | 137 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000007a6584097931b215a11f7413d95aaf645b8ac1dbd9b41e49db3f94 | 00000000009f73af5c5cee343bcbd2b3c364cf2849a108b8521d0e44ef66c327 | 135 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000face709b30aae127952e77fab23a2cb2762b5c80a45a089c91933252 | 0000000093f5776356fd4c0438de2dcb4971d44a98b4ffe1e027ccf4383c100d | 134 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000000066372e8fa967d3bb9854ffff078276a8edfdafc16288089b2bb2cd | 0000000000dc38e641e0a804f217d1a05139f9dcfdc4ed42ae7fcb7d1dfb2bdf | 133 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000000ad2f9589fd95cc5b06dbf31e37a7ee93ec24d75251fba184bd5db5e | 00000000246ada192c0dfbbf21639ac15632588c6837eea15fc5769f7aad7f29 | 132 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000008c5bae20dad3ce4d4ee58f8568815c7f1a2e4245aabea8799e619441 | 0000000092cb986b788943c854632242c98c95cf2e61e970d9aceafd6de089f7 | 132 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000092018c70e016a34155dd8739e95cbcb1873471375f44387b43ea133b | 0000000027b5cdac0b0aec557a0931e8db4527d454954f1a1a24634eaa97deb4 | 132 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000008d24a791d5002bb401e9028ca2f47ca3e95f689d5bf04345fb9e05c7 | 00000000231cc29111473df85569c8c13ff42b9fa2308da91e9e90677c3f4a56 | 132 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000002f46a1544c77493119619b10d8980ad33bab954adeee3c75e232c0d4 | 000000009ea8fb2f522d9df3d4a6f7b7fc8e8f86ef3983d4e5e25a3701bf7aa9 | 129 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000000000000452884b897e93eac8ee0ae8fc232ef71f70d51b3f75c96cb2 | 0000000000000001cd3b9b26b831ebacbed0d8b38d2d7046cda3fa5f58440977 | 129 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000ae564844cce06d19b23d24cc00cf6ba259761de0b4a107cd0957fbc9 | 000000002cbfbd983a7363525739e00a58ac2716c6ae78b360371a86318f71e7 | 128 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000566a689a721dd1965b56ef2f5747fe529e30d1d99d798a976f6f8140 | 00000000e6541ff86dbad9c9cad65da03fed072fc5bf18dd5ff1319ebe0b9737 | 127 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000b72ceaed015c62698031221165788ab29e7f60e213e8b2c2a6247bcc | 00000000a2762e5666e33efdd40843502cf9912f64be4ff0fdeb9cb73eff40cb | 127 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000031b01e7813d17569ad5963043584e2f72c9537a5875142d7ec2b5861 | 00000000199ddfb75856a000afa29279e1fc6d438d853ad5baeb1b1d012bf861 | 126 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000004c72affae39b49881cd993790d0c7364a1d15e015536da946cffda4c | 00000000e872e8bd3c764f2a1c01a90ffdb5d9d95fa92b45b4d3085b1ffedc75 | 124 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000557b874b6880c49db2969264ca0389859ee5bfc2260116734b9ceacb | 0000000098f48568e5a59fabfaa9c0c434e0e35e60f3867918d98a607c3d2706 | 122 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000c06b5dc93da5d7a66f996a5cf5e3043a8a42af09ad68f909b1d97e99 | 00000000001b3783ab66c48133632b90a9afea63354dbca73b6cb660d57b6194 | 122 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000000000000000b975fedb1fe62e271bd20d1fa74d2fe28dcfac6f761f3 | 0000000000000000000b5d9bcbd38c64e5a39bf4073f7a94348c1336618957ae | 122 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000000000000055af1b2188895541b3f229068be5ad63c2bc6a9aacbcd42a | 000000000000000016467960dc43772d1d05a0f3f038b81f779b3ad4136d295a | 122 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000769cadd838bbe424c8859e76a401c26ec22bb06ab3562d2fabcd7b0a | 00000000c4bd403cfb70989f5add22a588f017dfa919fee6cfb19e58bb9a98df | 121 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000c13610092f1b892b84e35235684c4737c25b848058a6d4388e2d1b2b | 0000000042562556b55941fa2a72c5965df573bf864d79f5dd65ef04996e2fe9 | 121 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000006a455b6e2d3c838f2942ae3896f913685660d96c985be7516d6b3ce2 | 000000005b8a14c28510e35529df893d73cba3c4f1c78c68f6029bf50c28ec8e | 121 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a27bf1a8d8ddae4596d1c34cdc8c29f7ee117744aa013173d2bf7f0a | 00000000377d5d78313b7e5fea4dd9d992dd05c08441241f59c6d2abc901a90a | 121 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000006f064062e711ae314f462b125caa23573c205ab39dbee2e582d730 | 000000000059f68a5e43cc152cd0e509ecd1cc8ac770b62da7be259f89b6a744 | 121 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000000f320e050c67c5c6d2f62660f820be4ee0d80bbab72e819d108ec43 | 00000000011e855947279cad92c26e9877de4bd6917a1de5e08f76cea95e1294 | 121 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000009152484ddc2192bc40c3ad656ab2b167307944d72f0411bb4b7e0099 | 000000003d378891a2f7324795311803239a5222ccb5a3241406756d218017e1 | 120 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000000000d379c7c8e9d5293e80128326ceff8f44e998a94e6fa5f221309a | 0000000000024fa2b47bbac000a73227730db9de1b2c7610a3b1c9675c90c917 | 120 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 00000000a2a7f323e0f4a69f58adb2429f5e3b5097e0a5134e094b87f6abf852 | 0000000046eb0934a822509c1011630427ee707f15d95bad7311d789da05a69b | 120 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000037df70bd3412132531ad910d2efb2ee55ea9d0351b552aade881ffbe | 0000000063689d97780b0e6e4f6d93a27770d50c93cc663cbf36ee662df14188 | 120 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 000000006d8adea045d994ff6d77f03e9b0134a32f807934ba9654d80cb7a9d4 | 000000006bc8272ef0ce21948a034ea13536586d068bb15ee648b198e9682ffd | 120 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| 0000000050e67c08b11edeaa9439fe1e78c7f4145e9ff13be9d0a466fa56aeb8 | 0000000007509c22a18706ddce980f2be2f56035ee29f2f732d03dff65a6719c | 120 m       |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+
| Occurrences: 152, Mean: 9.55 minutes, Standard Deviation: 14.13, Poisson Probability: 1 / 45550.53 hours                                          |
+------------------------------------------------------------------+------------------------------------------------------------------+-------------+

Conclusions

How often does the Bitcoin network see two consecutive blocks mined more than 2 hours apart from each other?

We should only see this occur once every 3 years using the Poisson distribution. However, according to the full population analysis, we see this occuring in practice far more often. Using the entire population data set, the probability of two consecutive blocks mined more than 2 hours apart from each other is 1 in every 4,924 blocks. This equates to about once a month.

How many times has the above happened so far in the history of Bitcoin?

According to the analysis of the full population set, this has occurred 152 times as of block height 748472. The longest period occuring on 2009-01-08 with block 00000000839a8e6886ab5951d76f411475428afc90947ee320161bbf18eb6048 at height 1 (immediately following the genesis block) clocking in at over 5 1/3 days.

Discussion

As time goes on, we should see blocks being mined more closely to the 10-minute target with a reducing frequency of large drifts such as over 2 hours. The majority of occurrences have happened in 2009 and during the early days of the network. As such, the distribution is skewed with a long right tail.

A great article on this phenomenon, so-called Bitcoin's "Poisson Paradox" which dives further into the topic.

Improvements

Possible future improvements:

• Zeroize sensitive data
• Saving a local copy of any blocks that have been previously queried
• Add more analytics