# Mining¶

Mining is the process of creating, validating, adding and distributing blocks.
Computers, and their administrators, that perform this service are referred to
as *miners*. Anyone computer on the network can become a miner. People are
incentivised to become miners because of the financial rewards. Mining
amazingly allows the Ethereum Classis system to be managed and secured in a
trustless decentralized manner.

## Proof Of Work Information¶

Valid blocks must contain certain numbers referred to as proof of work
information. These numbers are also referred to as *nonces*. Miners compete to
be the first to find this proof of work information and thereby add new blocks
to the blockchain. Finding proof of work information is intentionally made
difficult. This difficulty is a main reason for the security of the blockchain.

The difficult process of finding adequate nonces involves the following. Nonces must be found such that certain hashes of the blocks, with the nonces added, have numerical values below specified maxima. The only way to find such hashes is to simply try as many nonce guesses as possible until adequate hashes are found. The maxima are automatically adjusted to keep the average block addition time around 15 seconds. Ethash is the hashing algorithm in this process.

## Ethash¶

The Ethash hashing algorithm requires the determination of a certain extremely large directed acyclic graph that depends on block numbers. Quickly calculating several Ethash hashes requires storing the entire directed acyclic graph in memory. These large memory requirements thwart attempts to dominate the mining process by building application specific integrated circuits (ASICs).

## Uncle Blocks¶

In the contest to add blocks to the blockchain, the losing blocks can be leveraged to increase the security of the blockchain. These losing blocks, to be used this way, must have parent blocks that are at most six blocks from the growing end of the blockchain. Miners gain additional financial rewards when they mention the hashes of the headers of these losing blocks in blocks that are accepted. This uncle block system is referred to as the GHOST protocol.

Here is why uncle blocks increase the security of the blockchain. The mining contest will inevitably create multiple chains of blocks. The convention is that the official chain is the one that is the most difficult to reproduce. Adding uncle blocks increases the difficulty of reproducing the official chain.

Uncle blocks are especially useful when blocks are not propagating quickly throughout the network. This leads to many losing blocks as miners keep adding blocks to outdated versions of the official chain. As block creation times thereby increase, the security of the network decreases. This is fortunately mitigated with uncle blocks.

## Mining Pools¶

Because of the nature of the mining contest, the average expected mining rewards are proportional to the amount of computational resources dedicated to mining. There can still be variability in payout frequencies due to the random nature of the mining process. In order to deal with this variability, miners often join groups referred to as mining pools.

Some mining pools may lead to large amounts of mining resources in the control of a few individuals. Fortunately, there are trustless decentralized mining pools that avoid this risk.

## Mining Rewards¶

Mining rewards consists of three parts:

- Base Rewards
This part depends on the block numbers. It is paid with newly created funds. Every five million blocks (about 2.4 years) this part decreases by 20%. Initially it was 5 ETC. It changed to 4 ETC after block number five million and will continue to change in the future.

Define the block era E as a function of the block number N as follows (// denotes integer division):

```
E = (N - 1) // 5000000
```

Then the base reward is as follows:

```
5 ⋅ 0.8:superscript:`E`
```

- Uncle Rewards
This part depends on the number of uncle blocks included as well as the block numbers. It is also paid with newly created funds. Each block can include at most two uncle blocks. The reward for each uncle block is an additional 3.125% of the base reward.

For the block era E and number of uncles U, the total uncle reward is as follows:

```
0.03125 ⋅ U ⋅ (5 ⋅ 0.8:superscript:`E`)
```

After block number five million, miners that create the uncle blocks began getting this same reward per uncle block.

- Gas Rewards
This part depends on the transactions included. It is paid from the originating accounts. Miners execute the transactions and receive payments for the gas required. Each transactions specifies a price paid per unit gas.

For gas requirements G₁, G₂, G₃, … and corresponding gas prices P₁, P₂, P₃, …, the total gas reward is as follows:

```
G₁ ⋅ P₁ + G₂ ⋅ P₂ + G₃ ⋅ P₃ + …
```

Therefore, the total reward for creating a block is the following:

```
(1 + 0.03125 ⋅ U ) ⋅ (5 ⋅ 0.8:superscript:`E`) + G₁ ⋅ P₁ + G₂ ⋅ P₂ + G₃ ⋅ P₃ + …
```

Here is a Python script that uses this mining reward formula to calculate mining rewards:

```
#!/usr/bin/env python3
BASE_INITIAL = 5
BASE_PERCENT = 0.8
UNCLE_PERCENT = 0.03125
N_ERA_BLOCKS = 5e6
def mining_reward(block_number, num_uncles, gas_reqs, gas_prices):
"""
Calculates mining rewards from block information. The gas
information must be provided in lists or tuples. The gas
prices must be in ETC.
"""
era = (block_number - 1) // N_ERA_BLOCKS
base_reward = (BASE_PERCENT ** era) * BASE_INITIAL
uncle_reward = UNCLE_PERCENT * base_reward
uncle_rewards = num_uncles * uncle_reward
gas_rewards = 0
for (gas_req, gas_price) in zip(gas_reqs, gas_prices):
gas_rewards += gas_req * gas_price
return base_reward + uncle_rewards + gas_rewards
```

Here are some example calculations on real ETC blockchain data:

```
>>> mining_reward(5425392, 0, [], [])
4.0
>>> mining_reward(5423326, 1, [], [])
4.125
>>> mining_reward(5424471, 0, [36163, 36163] , [2e-8, 2e-8])
4.00144652
>>> mining_reward(5421363, 1, [21000, 21000, 21000, 21000, 21000], [5.5e-8, 2e-8, 2e-8, 1.6e-8, 1e-8])
4.127541
```

The mining reward formula bounds the supply of ETC. Notice only the base and uncle rewards increase the supply since the gas rewards just transfer existing funds. Because the uncle rewards vary, the eventual total supply of ETC can only be approximated.

The formula for the future increase in supply per era, assuming a constant number of uncle blocks, is the following:

```
5000000 ⋅ (1 + 2 ⋅ 0.03125 ⋅ U ) ⋅ (5 ⋅ 0.8:superscript:`E`)
```

The factor of 2 is necessary to include the uncle block creator rewards. The total supply can be estimated from this formula by adding the contributions for the remaining eras. Era 192, which will occur around the year 2474, is the last era which increases the supply.

Assuming no more uncle blocks gives a lower bound of about 198.3 million ETC. Assuming the maximum number of uncle blocks gives an upper bound of about 210.6 million ETC.