Ethash-R5
Overview
Ethash-R5 is a modified variant of the Ethash proof-of-work (PoW) algorithm, designed for the R5 blockchain. It builds on Ethereum’s original Ethash but introduces unique enhancements, including a 7-second block time target, a capped token supply, and an adjusted reward structure.
This document provides a technical breakdown of the algorithm, including its dataset mechanics, hashing process, and difficulty adjustments.
Algorithmic Changes in Ethash-R5
The Ethash-R5 algorithm maintains Ethash’s fundamental structure while implementing specific modifications:
7-second block time target enforced by an adjusted difficulty formula.
Super Epoch reward model with periodic reductions in miner rewards.
Modified uncle block policy: Uncles are valid but not rewarded.
Capped supply: No new issuance beyond block 1,290,406,400.
Extra sequential mixing rounds for additional security.
No support for Ethereum’s Shanghai and Cancun forks.
Key Components
1. Dataset & Cache Growth
Ethash-R5 retains Ethash’s dataset mechanics, where miners generate a dataset (DAG) that assists in the hashing process. However, the growth parameters have been modified:
Parameter
Value
Initial Dataset Size
1 GB (1 << 30)
Dataset Growth Per Epoch
8 MB (1 << 23)
Initial Cache Size
16 MB (1 << 24)
Cache Growth Per Epoch
128 KB (1 << 17)
Epoch Length
30,000 blocks
Mix Width
128 bytes
Hash Length
64 bytes
Hash Words
16 (32-bit words)
Dataset Parents
256
Cache Rounds
3
Accesses Per Loop
64
This dataset/cache size scaling ensures the network remains memory-hard, preventing ASIC dominance while keeping mining accessible for CPU and GPU miners.
2. Dataset & Cache Size Calculation
The dataset and cache sizes are determined by epoch number. Ethash-R5 precomputes values for the first 2,048 epochs, but after this limit, the sizes are calculated dynamically:
Cache Size Calculation
The cache size for an epoch n is computed as:
cache_size = cache_init_bytes + (cache_growth_bytes × n) − hash_byteswhere:
The resulting value is adjusted downward to the nearest prime number.
Dataset Size Calculation
Similarly, the dataset size is calculated as:
dataset_size =d ataset_init_bytes + (dataset_growth_bytes × n) − hash_bytesLike the cache size, this value is also adjusted downward to the nearest prime number.
For blocks beyond epoch 2,048, the dataset and cache sizes are calculated on demand.
3. DAG & Cache Generation
Cache Generation
The cache is a compressed representation of the dataset and is used for dataset lookup during mining.
Initial Seed: The cache is seeded using the Keccak-256 hash of a block’s epoch.
Keccak-512 Hashing: The seed undergoes multiple rounds of Keccak-512 hashing to populate the cache.
Mixing Rounds: Each entry in the cache is XOR-ed with values from random locations in previous cache entries.
Endian Correction: The cache undergoes a byte-swap step if the system is big-endian.
Dataset Generation
The dataset is derived from the cache and follows these steps:
Initial Mix: Each dataset element is initialised using a combination of cache values and its index.
Random Parent Selection: The dataset generation process selects 256 random cache parents.
FNV Hashing: The mix is iteratively FNV-hashed with parent values.
Final Keccak-512: A final Keccak-512 hashing step produces the dataset element.
Note: Unlike the cache, the dataset is not stored permanently—it is regenerated on demand.
4. Hashimoto PoW Function
The core mining process in Ethash-R5 uses the Hashimoto function, a memory-hard PoW function.
Hashimoto Steps
Header + Nonce Hashing:
A 40-byte seed is created by concatenating the block header hash and nonce.
This seed is hashed using Keccak-512.
Mix Initialisation:
The Keccak output is replicated across a 128-byte mix.
Memory Access Loop (64 iterations):
At each iteration:
A dataset parent is randomly selected.
The mix is FNV-hashed with the dataset parent.
Mix Compression:
The mix is compressed into a 32-byte digest using FNV hashing.
Extra Sequential Mixing Rounds (R5 Enhancement):
The digest undergoes 4 additional FNV-mixing rounds.
This increases sequential computation requirements, further reducing ASIC efficiency.
Final Hashing:
A final Keccak-256 hash is computed to generate the PoW output.
5. PoW Verification
To verify a submitted proof-of-work, Ethash-R5 follows the steps:
Recompute Seed:
The header hash and nonce are hashed together.
Run Hashimoto:
The Hashimoto function is executed using the miner’s provided nonce and mix digest.
Compare PoW Target:
The final hash must be below the difficulty target for the block to be valid.
Validation is lightweight, requiring only the cache rather than the full dataset.
6. Difficulty Adjustment
Ethash-R5 employs a modified difficulty algorithm designed to maintain a 7-second block time:
The difficulty adjusts every block based on the timestamp difference from the previous block.
Instead of Ethereum’s factor of 3, the adjustment divides difficulty by 2.
This modification ensures the network remains stable at 7-second blocks.
Security Enhancements
Ethash-R5 introduces additional security measures to mitigate ASIC and centralisation risks:
Extra Sequential Mixing:
Additional rounds of FNV mixing ensure that PoW computations remain sequential.
Memory-Hard Constraints:
The progressive dataset growth prevents fixed-hardware ASICs from gaining long-term advantages.
Strict Epoch Enforcement:
Each epoch’s dataset is unique, preventing reuse across epochs.
Supply Cap Enforcement:
Once the final issuance block (1,290,406,400) is reached, no more mining rewards are issued.
Go Implementation
// Copyright 2025 R5
// This file is part of the R5 Core library.
//
// This software is provided "as is", without warranty of any kind,
// express or implied, including but not limited to the warranties
// of merchantability, fitness for a particular purpose and
// noninfringement. In no event shall the authors or copyright
// holders be liable for any claim, damages, or other liability,
// whether in an action of contract, tort or otherwise, arising
// from, out of or in connection with the software or the use or
// other dealings in the software.
// ETHASH-R5 Implementation
// --------------------------------------------------------------
// Visit https://r5.network for more information
// Miner software developers should adjust for the 4 extra mixing
// rounds to generate correct hashes. Regular ETHASH miners won't
// work with ETHASH-R5 if not adjusted accordingly.
// --------------------------------------------------------------
package ethash
import (
"encoding/binary"
"hash"
"math/big"
"reflect"
"runtime"
"sync"
"sync/atomic"
"time"
"unsafe"
"github.com/r5-labs/r5-core/common"
"github.com/r5-labs/r5-core/common/bitutil"
"github.com/r5-labs/r5-core/crypto"
"github.com/r5-labs/r5-core/log"
"golang.org/x/crypto/sha3"
)
const (
datasetInitBytes = 1 << 30 // Bytes in dataset at genesis
datasetGrowthBytes = 1 << 23 // Dataset growth per epoch
cacheInitBytes = 1 << 24 // Bytes in cache at genesis
cacheGrowthBytes = 1 << 17 // Cache growth per epoch
epochLength = 30000 // Blocks per epoch
mixBytes = 128 // Width of mix
hashBytes = 64 // Hash length in bytes
hashWords = 16 // Number of 32 bit ints in a hash
datasetParents = 256 // Number of parents of each dataset element
cacheRounds = 3 // Number of rounds in cache production
loopAccesses = 64 // Number of accesses in hashimoto loop
)
// cacheSize returns the size of the ethash verification cache that belongs to a certain
// block number.
func cacheSize(block uint64) uint64 {
epoch := int(block / epochLength)
if epoch < maxEpoch {
return cacheSizes[epoch]
}
return calcCacheSize(epoch)
}
// calcCacheSize calculates the cache size for epoch. The cache size grows linearly,
// however, we always take the highest prime below the linearly growing threshold in order
// to reduce the risk of accidental regularities leading to cyclic behavior.
func calcCacheSize(epoch int) uint64 {
size := cacheInitBytes + cacheGrowthBytes*uint64(epoch) - hashBytes
for !new(big.Int).SetUint64(size / hashBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
size -= 2 * hashBytes
}
return size
}
// datasetSize returns the size of the ethash mining dataset that belongs to a certain
// block number.
func datasetSize(block uint64) uint64 {
epoch := int(block / epochLength)
if epoch < maxEpoch {
return datasetSizes[epoch]
}
return calcDatasetSize(epoch)
}
// calcDatasetSize calculates the dataset size for epoch. The dataset size grows linearly,
// however, we always take the highest prime below the linearly growing threshold in order
// to reduce the risk of accidental regularities leading to cyclic behavior.
func calcDatasetSize(epoch int) uint64 {
size := datasetInitBytes + datasetGrowthBytes*uint64(epoch) - mixBytes
for !new(big.Int).SetUint64(size / mixBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
size -= 2 * mixBytes
}
return size
}
// hasher is a repetitive hasher allowing the same hash data structures to be
// reused between hash runs instead of requiring new ones to be created.
type hasher func(dest []byte, data []byte)
// makeHasher creates a repetitive hasher, allowing the same hash data structures to
// be reused between hash runs instead of requiring new ones to be created. The returned
// function is not thread safe!
func makeHasher(h hash.Hash) hasher {
// sha3.state supports Read to get the sum, use it to avoid the overhead of Sum.
// Read alters the state but we reset the hash before every operation.
type readerHash interface {
hash.Hash
Read([]byte) (int, error)
}
rh, ok := h.(readerHash)
if !ok {
panic("can't find Read method on hash")
}
outputLen := rh.Size()
return func(dest []byte, data []byte) {
rh.Reset()
rh.Write(data)
rh.Read(dest[:outputLen])
}
}
// seedHash is the seed to use for generating a verification cache and the mining
// dataset.
func seedHash(block uint64) []byte {
seed := make([]byte, 32)
if block < epochLength {
return seed
}
keccak256 := makeHasher(sha3.NewLegacyKeccak256())
for i := 0; i < int(block/epochLength); i++ {
keccak256(seed, seed)
}
return seed
}
// generateCache creates a verification cache of a given size for an input seed.
// The cache production process involves first sequentially filling up 32 MB of
// memory, then performing two passes of Sergio Demian Lerner's RandMemoHash
// algorithm from Strict Memory Hard Hashing Functions (2014). The output is a
// set of 524288 64-byte values.
// This method places the result into dest in machine byte order.
func generateCache(dest []uint32, epoch uint64, seed []byte) {
// Print some debug logs to allow analysis on low end devices
logger := log.New("epoch", epoch)
start := time.Now()
defer func() {
elapsed := time.Since(start)
logFn := logger.Debug
if elapsed > 3*time.Second {
logFn = logger.Info
}
logFn("Generated ethash verification cache", "elapsed", common.PrettyDuration(elapsed))
}()
// Convert our destination slice to a byte buffer
var cache []byte
cacheHdr := (*reflect.SliceHeader)(unsafe.Pointer(&cache))
dstHdr := (*reflect.SliceHeader)(unsafe.Pointer(&dest))
cacheHdr.Data = dstHdr.Data
cacheHdr.Len = dstHdr.Len * 4
cacheHdr.Cap = dstHdr.Cap * 4
// Calculate the number of theoretical rows (we'll store in one buffer nonetheless)
size := uint64(len(cache))
rows := int(size) / hashBytes
// Start a monitoring goroutine to report progress on low end devices
var progress atomic.Uint32
done := make(chan struct{})
defer close(done)
go func() {
for {
select {
case <-done:
return
case <-time.After(3 * time.Second):
logger.Info("Generating ethash verification cache", "percentage", progress.Load()*100/uint32(rows)/(cacheRounds+1), "elapsed", common.PrettyDuration(time.Since(start)))
}
}
}()
// Create a hasher to reuse between invocations
keccak512 := makeHasher(sha3.NewLegacyKeccak512())
// Sequentially produce the initial dataset
keccak512(cache, seed)
for offset := uint64(hashBytes); offset < size; offset += hashBytes {
keccak512(cache[offset:], cache[offset-hashBytes:offset])
progress.Add(1)
}
// Use a low-round version of randmemohash
temp := make([]byte, hashBytes)
for i := 0; i < cacheRounds; i++ {
for j := 0; j < rows; j++ {
var (
srcOff = ((j - 1 + rows) % rows) * hashBytes
dstOff = j * hashBytes
xorOff = (binary.LittleEndian.Uint32(cache[dstOff:]) % uint32(rows)) * hashBytes
)
bitutil.XORBytes(temp, cache[srcOff:srcOff+hashBytes], cache[xorOff:xorOff+hashBytes])
keccak512(cache[dstOff:], temp)
progress.Add(1)
}
}
// Swap the byte order on big endian systems and return
if !isLittleEndian() {
swap(cache)
}
}
// swap changes the byte order of the buffer assuming a uint32 representation.
func swap(buffer []byte) {
for i := 0; i < len(buffer); i += 4 {
binary.BigEndian.PutUint32(buffer[i:], binary.LittleEndian.Uint32(buffer[i:]))
}
}
// fnv is an algorithm inspired by the FNV hash, which in some cases is used as
// a non-associative substitute for XOR. Note that we multiply the prime with
// the full 32-bit input, in contrast with the FNV-1 spec which multiplies the
// prime with one byte (octet) in turn.
func fnv(a, b uint32) uint32 {
return a*0x01000193 ^ b
}
// fnvHash mixes in data into mix using the ethash fnv method.
func fnvHash(mix []uint32, data []uint32) {
for i := 0; i < len(mix); i++ {
mix[i] = mix[i]*0x01000193 ^ data[i]
}
}
// generateDatasetItem combines data from 256 pseudorandomly selected cache nodes,
// and hashes that to compute a single dataset node.
func generateDatasetItem(cache []uint32, index uint32, keccak512 hasher) []byte {
// Calculate the number of theoretical rows (we use one buffer nonetheless)
rows := uint32(len(cache) / hashWords)
// Initialize the mix
mix := make([]byte, hashBytes)
binary.LittleEndian.PutUint32(mix, cache[(index%rows)*hashWords]^index)
for i := 1; i < hashWords; i++ {
binary.LittleEndian.PutUint32(mix[i*4:], cache[(index%rows)*hashWords+uint32(i)])
}
keccak512(mix, mix)
// Convert the mix to uint32s to avoid constant bit shifting
intMix := make([]uint32, hashWords)
for i := 0; i < len(intMix); i++ {
intMix[i] = binary.LittleEndian.Uint32(mix[i*4:])
}
// fnv it with a lot of random cache nodes based on index
for i := uint32(0); i < datasetParents; i++ {
parent := fnv(index^i, intMix[i%16]) % rows
fnvHash(intMix, cache[parent*hashWords:])
}
// Flatten the uint32 mix into a binary one and return
for i, val := range intMix {
binary.LittleEndian.PutUint32(mix[i*4:], val)
}
keccak512(mix, mix)
return mix
}
// generateDataset generates the entire ethash dataset for mining.
// This method places the result into dest in machine byte order.
func generateDataset(dest []uint32, epoch uint64, cache []uint32) {
// Print some debug logs to allow analysis on low end devices
logger := log.New("epoch", epoch)
start := time.Now()
defer func() {
elapsed := time.Since(start)
logFn := logger.Debug
if elapsed > 3*time.Second {
logFn = logger.Info
}
logFn("Generated ethash verification cache", "elapsed", common.PrettyDuration(elapsed))
}()
// Figure out whether the bytes need to be swapped for the machine
swapped := !isLittleEndian()
// Convert our destination slice to a byte buffer
var dataset []byte
datasetHdr := (*reflect.SliceHeader)(unsafe.Pointer(&dataset))
destHdr := (*reflect.SliceHeader)(unsafe.Pointer(&dest))
datasetHdr.Data = destHdr.Data
datasetHdr.Len = destHdr.Len * 4
datasetHdr.Cap = destHdr.Cap * 4
// Generate the dataset on many goroutines since it takes a while
threads := runtime.NumCPU()
size := uint64(len(dataset))
var pend sync.WaitGroup
pend.Add(threads)
var progress atomic.Uint64
for i := 0; i < threads; i++ {
go func(id int) {
defer pend.Done()
// Create a hasher to reuse between invocations
keccak512 := makeHasher(sha3.NewLegacyKeccak512())
// Calculate the data segment this thread should generate
batch := (size + hashBytes*uint64(threads) - 1) / (hashBytes * uint64(threads))
first := uint64(id) * batch
limit := first + batch
if limit > size/hashBytes {
limit = size / hashBytes
}
// Calculate the dataset segment
percent := size / hashBytes / 100
for index := first; index < limit; index++ {
item := generateDatasetItem(cache, uint32(index), keccak512)
if swapped {
swap(item)
}
copy(dataset[index*hashBytes:], item)
if status := progress.Add(1); status%percent == 0 {
logger.Info("Generating DAG in progress", "percentage", (status*100)/(size/hashBytes), "elapsed", common.PrettyDuration(time.Since(start)))
}
}
}(i)
}
// Wait for all the generators to finish and return
pend.Wait()
}
// hashimoto aggregates data from the full dataset in order to produce our final
// value for a particular header hash and nonce.
func hashimoto(hash []byte, nonce uint64, size uint64, lookup func(index uint32) []uint32) ([]byte, []byte) {
// 1. Standard Hashimoto (inherited from standard Ethash) with extra sequential dependency
rows := uint32(size / mixBytes)
// Combine header+nonce into a 40-byte seed
seed := make([]byte, 40)
copy(seed, hash)
binary.LittleEndian.PutUint64(seed[32:], nonce)
// Keccak-512 of the seed
seed = crypto.Keccak512(seed)
seedHead := binary.LittleEndian.Uint32(seed)
// Initialize the mix: replicate the 512-bit seed across mix
mix := make([]uint32, mixBytes/4)
for i := 0; i < len(mix); i++ {
mix[i] = binary.LittleEndian.Uint32(seed[(i%16)*4:])
}
// Main loop: add sequential dependency and a conditional branch to hinder GPU parallelism
temp := make([]uint32, len(mix))
// Start with a sequential dependency variable initialized from seedHead.
seqDep := seedHead
for i := 0; i < loopAccesses; i++ {
// Update the sequential dependency with a value from mix.
seqDep = fnv(seqDep, mix[i%len(mix)])
// Use seqDep (instead of seedHead) to calculate parent index.
parent := fnv(uint32(i)^seqDep, mix[i%len(mix)]) % rows
for j := uint32(0); j < mixBytes/hashBytes; j++ {
copy(temp[j*hashWords:], lookup(2*parent+j))
}
// Insert a data-dependent branch to force divergence:
if (mix[0] & 0x1) == 1 {
// Extra mixing on the first element to force serial dependency.
mix[0] = fnv(mix[0], temp[0])
}
fnvHash(mix, temp)
}
// Compress mix to a 32-byte digest.
for i := 0; i < len(mix); i += 4 {
mix[i/4] = fnv(fnv(fnv(mix[i], mix[i+1]), mix[i+2]), mix[i+3])
}
mix = mix[:len(mix)/4]
digest := make([]byte, 32)
for i, val := range mix {
binary.LittleEndian.PutUint32(digest[i*4:], val)
}
// 2. Ethash-R5 extension: four extra mixing rounds with added sequential work
// (Keccak256 ∘ FNV_Mix)^4 applied to the digest
extraKeccak := makeHasher(sha3.NewLegacyKeccak256())
for round := 0; round < 4; round++ {
// Interpret digest as array of uint32
extra := make([]uint32, len(digest)/4)
for i := 0; i < len(extra); i++ {
extra[i] = binary.LittleEndian.Uint32(digest[i*4:])
}
// Add a sequential inner loop to further force serial computation.
for k := 0; k < 3; k++ {
extra[0] = fnv(extra[0], extra[len(extra)-1])
}
// FNV-mix the array with itself
fnvHash(extra, extra)
// Convert back to bytes
for i, val := range extra {
binary.LittleEndian.PutUint32(digest[i*4:], val)
}
// Data-dependent branch: if the least significant bit of digest[0] is 0, perform an extra Keccak mix.
if (digest[0] & 1) == 0 {
tmp := make([]byte, len(digest))
extraKeccak(tmp, digest)
copy(digest, tmp)
}
}
// -----------------------------------------------------------------------
// 3. Final hash remains the same: Keccak256(seed || digest)
// -----------------------------------------------------------------------
finalHash := crypto.Keccak256(append(seed, digest...))
return digest, finalHash
}
// hashimotoLight aggregates data from the full dataset (using only a small
// in-memory cache) in order to produce our final value for a particular header
// hash and nonce.
func hashimotoLight(size uint64, cache []uint32, hash []byte, nonce uint64) ([]byte, []byte) {
keccak512 := makeHasher(sha3.NewLegacyKeccak512())
lookup := func(index uint32) []uint32 {
rawData := generateDatasetItem(cache, index, keccak512)
data := make([]uint32, len(rawData)/4)
for i := 0; i < len(data); i++ {
data[i] = binary.LittleEndian.Uint32(rawData[i*4:])
}
return data
}
return hashimoto(hash, nonce, size, lookup)
}
// hashimotoFull aggregates data from the full dataset (using the full in-memory
// dataset) in order to produce our final value for a particular header hash and
// nonce.
func hashimotoFull(dataset []uint32, hash []byte, nonce uint64) ([]byte, []byte) {
lookup := func(index uint32) []uint32 {
offset := index * hashWords
return dataset[offset : offset+hashWords]
}
return hashimoto(hash, nonce, uint64(len(dataset))*4, lookup)
}
const maxEpoch = 2048
// datasetSizes is a lookup table for the ethash dataset size for the first 2048
// epochs (i.e. 61440000 blocks).
var datasetSizes = [maxEpoch]uint64{
1073739904, 1082130304, 1090514816, 1098906752, 1107293056,
1115684224, 1124070016, 1132461952, 1140849536, 1149232768,
1157627776, 1166013824, 1174404736, 1182786944, 1191180416,
1199568512, 1207958912, 1216345216, 1224732032, 1233124736,
1241513344, 1249902464, 1258290304, 1266673792, 1275067264,
1283453312, 1291844992, 1300234112, 1308619904, 1317010048,
1325397376, 1333787776, 1342176128, 1350561664, 1358954368,
1367339392, 1375731584, 1384118144, 1392507008, 1400897408,
1409284736, 1417673344, 1426062464, 1434451072, 1442839168,
1451229056, 1459615616, 1468006016, 1476394112, 1484782976,
1493171584, 1501559168, 1509948032, 1518337664, 1526726528,
1535114624, 1543503488, 1551892096, 1560278656, 1568669056,
1577056384, 1585446272, 1593831296, 1602219392, 1610610304,
1619000192, 1627386752, 1635773824, 1644164224, 1652555648,
1660943488, 1669332608, 1677721216, 1686109312, 1694497664,
1702886272, 1711274624, 1719661184, 1728047744, 1736434816,
1744829056, 1753218944, 1761606272, 1769995904, 1778382464,
1786772864, 1795157888, 1803550592, 1811937664, 1820327552,
1828711552, 1837102976, 1845488768, 1853879936, 1862269312,
1870656896, 1879048064, 1887431552, 1895825024, 1904212096,
1912601216, 1920988544, 1929379456, 1937765504, 1946156672,
1954543232, 1962932096, 1971321728, 1979707264, 1988093056,
1996487552, 2004874624, 2013262208, 2021653888, 2030039936,
2038430848, 2046819968, 2055208576, 2063596672, 2071981952,
2080373632, 2088762752, 2097149056, 2105539712, 2113928576,
2122315136, 2130700672, 2139092608, 2147483264, 2155872128,
2164257664, 2172642176, 2181035392, 2189426048, 2197814912,
2206203008, 2214587264, 2222979712, 2231367808, 2239758208,
2248145024, 2256527744, 2264922752, 2273312128, 2281701248,
2290086272, 2298476672, 2306867072, 2315251072, 2323639168,
2332032128, 2340420224, 2348808064, 2357196416, 2365580416,
2373966976, 2382363008, 2390748544, 2399139968, 2407530368,
2415918976, 2424307328, 2432695424, 2441084288, 2449472384,
2457861248, 2466247808, 2474637184, 2483026816, 2491414144,
2499803776, 2508191872, 2516582272, 2524970368, 2533359232,
2541743488, 2550134144, 2558525056, 2566913408, 2575301504,
2583686528, 2592073856, 2600467328, 2608856192, 2617240448,
2625631616, 2634022016, 2642407552, 2650796416, 2659188352,
2667574912, 2675965312, 2684352896, 2692738688, 2701130624,
2709518464, 2717907328, 2726293376, 2734685056, 2743073152,
2751462016, 2759851648, 2768232832, 2776625536, 2785017728,
2793401984, 2801794432, 2810182016, 2818571648, 2826959488,
2835349376, 2843734144, 2852121472, 2860514432, 2868900992,
2877286784, 2885676928, 2894069632, 2902451584, 2910843008,
2919234688, 2927622784, 2936011648, 2944400768, 2952789376,
2961177728, 2969565568, 2977951616, 2986338944, 2994731392,
3003120256, 3011508352, 3019895936, 3028287104, 3036675968,
3045063808, 3053452928, 3061837696, 3070228352, 3078615424,
3087003776, 3095394944, 3103782272, 3112173184, 3120562048,
3128944768, 3137339264, 3145725056, 3154109312, 3162505088,
3170893184, 3179280256, 3187669376, 3196056704, 3204445568,
3212836736, 3221224064, 3229612928, 3238002304, 3246391168,
3254778496, 3263165824, 3271556224, 3279944576, 3288332416,
3296719232, 3305110912, 3313500032, 3321887104, 3330273152,
3338658944, 3347053184, 3355440512, 3363827072, 3372220288,
3380608384, 3388997504, 3397384576, 3405774208, 3414163072,
3422551936, 3430937984, 3439328384, 3447714176, 3456104576,
3464493952, 3472883584, 3481268864, 3489655168, 3498048896,
3506434432, 3514826368, 3523213952, 3531603584, 3539987072,
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15040768384, 15049154944, 15057549184, 15065939072, 15074328448,
15082715008, 15091104128, 15099493504, 15107879296, 15116269184,
15124659584, 15133042304, 15141431936, 15149824384, 15158214272,
15166602368, 15174991232, 15183378304, 15191760512, 15200154496,
15208542592, 15216931712, 15225323392, 15233708416, 15242098048,
15250489216, 15258875264, 15267265408, 15275654528, 15284043136,
15292431488, 15300819584, 15309208192, 15317596544, 15325986176,
15334374784, 15342763648, 15351151744, 15359540608, 15367929728,
15376318336, 15384706432, 15393092992, 15401481856, 15409869952,
15418258816, 15426649984, 15435037568, 15443425664, 15451815296,
15460203392, 15468589184, 15476979328, 15485369216, 15493755776,
15502146944, 15510534272, 15518924416, 15527311232, 15535699072,
15544089472, 15552478336, 15560866688, 15569254528, 15577642624,
15586031488, 15594419072, 15602809472, 15611199104, 15619586432,
15627975296, 15636364928, 15644753792, 15653141888, 15661529216,
15669918848, 15678305152, 15686696576, 15695083136, 15703474048,
15711861632, 15720251264, 15728636288, 15737027456, 15745417088,
15753804928, 15762194048, 15770582656, 15778971008, 15787358336,
15795747712, 15804132224, 15812523392, 15820909696, 15829300096,
15837691264, 15846071936, 15854466944, 15862855808, 15871244672,
15879634816, 15888020608, 15896409728, 15904799104, 15913185152,
15921577088, 15929966464, 15938354816, 15946743424, 15955129472,
15963519872, 15971907968, 15980296064, 15988684928, 15997073024,
16005460864, 16013851264, 16022241152, 16030629248, 16039012736,
16047406976, 16055794816, 16064181376, 16072571264, 16080957824,
16089346688, 16097737856, 16106125184, 16114514816, 16122904192,
16131292544, 16139678848, 16148066944, 16156453504, 16164839552,
16173236096, 16181623424, 16190012032, 16198401152, 16206790528,
16215177344, 16223567744, 16231956352, 16240344704, 16248731008,
16257117824, 16265504384, 16273898624, 16282281856, 16290668672,
16299064192, 16307449216, 16315842176, 16324230016, 16332613504,
16341006464, 16349394304, 16357783168, 16366172288, 16374561664,
16382951296, 16391337856, 16399726208, 16408116352, 16416505472,
16424892032, 16433282176, 16441668224, 16450058624, 16458448768,
16466836864, 16475224448, 16483613056, 16492001408, 16500391808,
16508779648, 16517166976, 16525555328, 16533944192, 16542330752,
16550719616, 16559110528, 16567497088, 16575888512, 16584274816,
16592665472, 16601051008, 16609442944, 16617832064, 16626218624,
16634607488, 16642996096, 16651385728, 16659773824, 16668163712,
16676552576, 16684938112, 16693328768, 16701718144, 16710095488,
16718492288, 16726883968, 16735272832, 16743661184, 16752049792,
16760436608, 16768827008, 16777214336, 16785599104, 16793992832,
16802381696, 16810768768, 16819151744, 16827542656, 16835934848,
16844323712, 16852711552, 16861101952, 16869489536, 16877876864,
16886265728, 16894653056, 16903044736, 16911431296, 16919821696,
16928207488, 16936592768, 16944987776, 16953375616, 16961763968,
16970152832, 16978540928, 16986929536, 16995319168, 17003704448,
17012096896, 17020481152, 17028870784, 17037262208, 17045649536,
17054039936, 17062426496, 17070814336, 17079205504, 17087592064,
17095978112, 17104369024, 17112759424, 17121147776, 17129536384,
17137926016, 17146314368, 17154700928, 17163089792, 17171480192,
17179864192, 17188256896, 17196644992, 17205033856, 17213423488,
17221811072, 17230198912, 17238588032, 17246976896, 17255360384,
17263754624, 17272143232, 17280530048, 17288918912, 17297309312,
17305696384, 17314085504, 17322475136, 17330863744, 17339252096,
17347640192, 17356026496, 17364413824, 17372796544, 17381190016,
17389583488, 17397972608, 17406360704, 17414748544, 17423135872,
17431527296, 17439915904, 17448303232, 17456691584, 17465081728,
17473468288, 17481857408, 17490247552, 17498635904, 17507022464,
17515409024, 17523801728, 17532189824, 17540577664, 17548966016,
17557353344, 17565741184, 17574131584, 17582519168, 17590907008,
17599296128, 17607687808, 17616076672, 17624455808, 17632852352,
17641238656, 17649630848, 17658018944, 17666403968, 17674794112,
17683178368, 17691573376, 17699962496, 17708350592, 17716739968,
17725126528, 17733517184, 17741898112, 17750293888, 17758673024,
17767070336, 17775458432, 17783848832, 17792236928, 17800625536,
17809012352, 17817402752, 17825785984, 17834178944, 17842563968,
17850955648, 17859344512, 17867732864, 17876119424, 17884511872,
17892900224, 17901287296, 17909677696, 17918058112, 17926451072,
17934843776, 17943230848, 17951609216, 17960008576, 17968397696,
17976784256, 17985175424, 17993564032, 18001952128, 18010339712,
18018728576, 18027116672, 18035503232, 18043894144, 18052283264,
18060672128, 18069056384, 18077449856, 18085837184, 18094225792,
18102613376, 18111004544, 18119388544, 18127781248, 18136170368,
18144558976, 18152947328, 18161336192, 18169724288, 18178108544,
18186498944, 18194886784, 18203275648, 18211666048, 18220048768,
18228444544, 18236833408, 18245220736}
// cacheSizes is a lookup table for the ethash verification cache size for the
// first 2048 epochs (i.e. 61440000 blocks).
var cacheSizes = [maxEpoch]uint64{
16776896, 16907456, 17039296, 17170112, 17301056, 17432512, 17563072,
17693888, 17824192, 17955904, 18087488, 18218176, 18349504, 18481088,
18611392, 18742336, 18874304, 19004224, 19135936, 19267264, 19398208,
19529408, 19660096, 19791424, 19922752, 20053952, 20184896, 20315968,
20446912, 20576576, 20709184, 20840384, 20971072, 21102272, 21233216,
21364544, 21494848, 21626816, 21757376, 21887552, 22019392, 22151104,
22281536, 22412224, 22543936, 22675264, 22806464, 22935872, 23068096,
23198272, 23330752, 23459008, 23592512, 23723968, 23854912, 23986112,
24116672, 24247616, 24378688, 24509504, 24640832, 24772544, 24903488,
25034432, 25165376, 25296704, 25427392, 25558592, 25690048, 25820096,
25951936, 26081728, 26214208, 26345024, 26476096, 26606656, 26737472,
26869184, 26998208, 27131584, 27262528, 27393728, 27523904, 27655744,
27786688, 27917888, 28049344, 28179904, 28311488, 28441792, 28573504,
28700864, 28835648, 28966208, 29096768, 29228608, 29359808, 29490752,
29621824, 29752256, 29882816, 30014912, 30144448, 30273728, 30406976,
30538432, 30670784, 30799936, 30932672, 31063744, 31195072, 31325248,
31456192, 31588288, 31719232, 31850432, 31981504, 32110784, 32243392,
32372672, 32505664, 32636608, 32767808, 32897344, 33029824, 33160768,
33289664, 33423296, 33554368, 33683648, 33816512, 33947456, 34076992,
34208704, 34340032, 34471744, 34600256, 34734016, 34864576, 34993984,
35127104, 35258176, 35386688, 35518528, 35650624, 35782336, 35910976,
36044608, 36175808, 36305728, 36436672, 36568384, 36699968, 36830656,
36961984, 37093312, 37223488, 37355072, 37486528, 37617472, 37747904,
37879232, 38009792, 38141888, 38272448, 38403392, 38535104, 38660672,
38795584, 38925632, 39059264, 39190336, 39320768, 39452096, 39581632,
39713984, 39844928, 39974848, 40107968, 40238144, 40367168, 40500032,
40631744, 40762816, 40894144, 41023552, 41155904, 41286208, 41418304,
41547712, 41680448, 41811904, 41942848, 42073792, 42204992, 42334912,
42467008, 42597824, 42729152, 42860096, 42991552, 43122368, 43253696,
43382848, 43515712, 43646912, 43777088, 43907648, 44039104, 44170432,
44302144, 44433344, 44564288, 44694976, 44825152, 44956864, 45088448,
45219008, 45350464, 45481024, 45612608, 45744064, 45874496, 46006208,
46136768, 46267712, 46399424, 46529344, 46660672, 46791488, 46923328,
47053504, 47185856, 47316928, 47447872, 47579072, 47710144, 47839936,
47971648, 48103232, 48234176, 48365248, 48496192, 48627136, 48757312,
48889664, 49020736, 49149248, 49283008, 49413824, 49545152, 49675712,
49807168, 49938368, 50069056, 50200256, 50331584, 50462656, 50593472,
50724032, 50853952, 50986048, 51117632, 51248576, 51379904, 51510848,
51641792, 51773248, 51903296, 52035136, 52164032, 52297664, 52427968,
52557376, 52690112, 52821952, 52952896, 53081536, 53213504, 53344576,
53475776, 53608384, 53738816, 53870528, 54000832, 54131776, 54263744,
54394688, 54525248, 54655936, 54787904, 54918592, 55049152, 55181248,
55312064, 55442752, 55574336, 55705024, 55836224, 55967168, 56097856,
56228672, 56358592, 56490176, 56621888, 56753728, 56884928, 57015488,
57146816, 57278272, 57409216, 57540416, 57671104, 57802432, 57933632,
58064576, 58195264, 58326976, 58457408, 58588864, 58720192, 58849984,
58981696, 59113024, 59243456, 59375552, 59506624, 59637568, 59768512,
59897792, 60030016, 60161984, 60293056, 60423872, 60554432, 60683968,
60817216, 60948032, 61079488, 61209664, 61341376, 61471936, 61602752,
61733696, 61865792, 61996736, 62127808, 62259136, 62389568, 62520512,
62651584, 62781632, 62910784, 63045056, 63176128, 63307072, 63438656,
63569216, 63700928, 63831616, 63960896, 64093888, 64225088, 64355392,
64486976, 64617664, 64748608, 64879424, 65009216, 65142464, 65273792,
65402816, 65535424, 65666752, 65797696, 65927744, 66060224, 66191296,
66321344, 66453056, 66584384, 66715328, 66846656, 66977728, 67108672,
67239104, 67370432, 67501888, 67631296, 67763776, 67895104, 68026304,
68157248, 68287936, 68419264, 68548288, 68681408, 68811968, 68942912,
69074624, 69205568, 69337024, 69467584, 69599168, 69729472, 69861184,
69989824, 70122944, 70253888, 70385344, 70515904, 70647232, 70778816,
70907968, 71040832, 71171648, 71303104, 71432512, 71564992, 71695168,
71826368, 71958464, 72089536, 72219712, 72350144, 72482624, 72613568,
72744512, 72875584, 73006144, 73138112, 73268672, 73400128, 73530944,
73662272, 73793344, 73924544, 74055104, 74185792, 74316992, 74448832,
74579392, 74710976, 74841664, 74972864, 75102784, 75233344, 75364544,
75497024, 75627584, 75759296, 75890624, 76021696, 76152256, 76283072,
76414144, 76545856, 76676672, 76806976, 76937792, 77070016, 77200832,
77331392, 77462464, 77593664, 77725376, 77856448, 77987776, 78118336,
78249664, 78380992, 78511424, 78642496, 78773056, 78905152, 79033664,
79166656, 79297472, 79429568, 79560512, 79690816, 79822784, 79953472,
80084672, 80214208, 80346944, 80477632, 80608576, 80740288, 80870848,
81002048, 81133504, 81264448, 81395648, 81525952, 81657536, 81786304,
81919808, 82050112, 82181312, 82311616, 82443968, 82573376, 82705984,
82835776, 82967744, 83096768, 83230528, 83359552, 83491264, 83622464,
83753536, 83886016, 84015296, 84147776, 84277184, 84409792, 84540608,
84672064, 84803008, 84934336, 85065152, 85193792, 85326784, 85458496,
85589312, 85721024, 85851968, 85982656, 86112448, 86244416, 86370112,
86506688, 86637632, 86769344, 86900672, 87031744, 87162304, 87293632,
87424576, 87555392, 87687104, 87816896, 87947968, 88079168, 88211264,
88341824, 88473152, 88603712, 88735424, 88862912, 88996672, 89128384,
89259712, 89390272, 89521984, 89652544, 89783872, 89914816, 90045376,
90177088, 90307904, 90438848, 90569152, 90700096, 90832832, 90963776,
91093696, 91223744, 91356992, 91486784, 91618496, 91749824, 91880384,
92012224, 92143552, 92273344, 92405696, 92536768, 92666432, 92798912,
92926016, 93060544, 93192128, 93322816, 93453632, 93583936, 93715136,
93845056, 93977792, 94109504, 94240448, 94371776, 94501184, 94632896,
94764224, 94895552, 95023424, 95158208, 95287744, 95420224, 95550016,
95681216, 95811904, 95943872, 96075328, 96203584, 96337856, 96468544,
96599744, 96731072, 96860992, 96992576, 97124288, 97254848, 97385536,
97517248, 97647808, 97779392, 97910464, 98041408, 98172608, 98303168,
98434496, 98565568, 98696768, 98827328, 98958784, 99089728, 99220928,
99352384, 99482816, 99614272, 99745472, 99876416, 100007104,
100138048, 100267072, 100401088, 100529984, 100662592, 100791872,
100925248, 101056064, 101187392, 101317952, 101449408, 101580608,
101711296, 101841728, 101973824, 102104896, 102235712, 102366016,
102498112, 102628672, 102760384, 102890432, 103021888, 103153472,
103284032, 103415744, 103545152, 103677248, 103808576, 103939648,
104070976, 104201792, 104332736, 104462528, 104594752, 104725952,
104854592, 104988608, 105118912, 105247808, 105381184, 105511232,
105643072, 105774784, 105903296, 106037056, 106167872, 106298944,
106429504, 106561472, 106691392, 106822592, 106954304, 107085376,
107216576, 107346368, 107478464, 107609792, 107739712, 107872192,
108003136, 108131392, 108265408, 108396224, 108527168, 108657344,
108789568, 108920384, 109049792, 109182272, 109312576, 109444928,
109572928, 109706944, 109837888, 109969088, 110099648, 110230976,
110362432, 110492992, 110624704, 110755264, 110886208, 111017408,
111148864, 111279296, 111410752, 111541952, 111673024, 111803456,
111933632, 112066496, 112196416, 112328512, 112457792, 112590784,
112715968, 112852672, 112983616, 113114944, 113244224, 113376448,
113505472, 113639104, 113770304, 113901376, 114031552, 114163264,
114294592, 114425536, 114556864, 114687424, 114818624, 114948544,
115080512, 115212224, 115343296, 115473472, 115605184, 115736128,
115867072, 115997248, 116128576, 116260288, 116391488, 116522944,
116652992, 116784704, 116915648, 117046208, 117178304, 117308608,
117440192, 117569728, 117701824, 117833024, 117964096, 118094656,
118225984, 118357312, 118489024, 118617536, 118749632, 118882112,
119012416, 119144384, 119275328, 119406016, 119537344, 119668672,
119798464, 119928896, 120061376, 120192832, 120321728, 120454336,
120584512, 120716608, 120848192, 120979136, 121109056, 121241408,
121372352, 121502912, 121634752, 121764416, 121895744, 122027072,
122157632, 122289088, 122421184, 122550592, 122682944, 122813888,
122945344, 123075776, 123207488, 123338048, 123468736, 123600704,
123731264, 123861952, 123993664, 124124608, 124256192, 124386368,
124518208, 124649024, 124778048, 124911296, 125041088, 125173696,
125303744, 125432896, 125566912, 125696576, 125829056, 125958592,
126090304, 126221248, 126352832, 126483776, 126615232, 126746432,
126876608, 127008704, 127139392, 127270336, 127401152, 127532224,
127663552, 127794752, 127925696, 128055232, 128188096, 128319424,
128449856, 128581312, 128712256, 128843584, 128973632, 129103808,
129236288, 129365696, 129498944, 129629888, 129760832, 129892288,
130023104, 130154048, 130283968, 130416448, 130547008, 130678336,
130807616, 130939456, 131071552, 131202112, 131331776, 131464384,
131594048, 131727296, 131858368, 131987392, 132120256, 132250816,
132382528, 132513728, 132644672, 132774976, 132905792, 133038016,
133168832, 133299392, 133429312, 133562048, 133692992, 133823296,
133954624, 134086336, 134217152, 134348608, 134479808, 134607296,
134741056, 134872384, 135002944, 135134144, 135265472, 135396544,
135527872, 135659072, 135787712, 135921472, 136052416, 136182848,
136313792, 136444864, 136576448, 136707904, 136837952, 136970048,
137099584, 137232064, 137363392, 137494208, 137625536, 137755712,
137887424, 138018368, 138149824, 138280256, 138411584, 138539584,
138672832, 138804928, 138936128, 139066688, 139196864, 139328704,
139460032, 139590208, 139721024, 139852864, 139984576, 140115776,
140245696, 140376512, 140508352, 140640064, 140769856, 140902336,
141032768, 141162688, 141294016, 141426496, 141556544, 141687488,
141819584, 141949888, 142080448, 142212544, 142342336, 142474432,
142606144, 142736192, 142868288, 142997824, 143129408, 143258944,
143392448, 143523136, 143653696, 143785024, 143916992, 144045632,
144177856, 144309184, 144440768, 144570688, 144701888, 144832448,
144965056, 145096384, 145227584, 145358656, 145489856, 145620928,
145751488, 145883072, 146011456, 146144704, 146275264, 146407232,
146538176, 146668736, 146800448, 146931392, 147062336, 147193664,
147324224, 147455936, 147586624, 147717056, 147848768, 147979456,
148110784, 148242368, 148373312, 148503232, 148635584, 148766144,
148897088, 149028416, 149159488, 149290688, 149420224, 149551552,
149683136, 149814976, 149943616, 150076352, 150208064, 150338624,
150470464, 150600256, 150732224, 150862784, 150993088, 151125952,
151254976, 151388096, 151519168, 151649728, 151778752, 151911104,
152042944, 152174144, 152304704, 152435648, 152567488, 152698816,
152828992, 152960576, 153091648, 153222976, 153353792, 153484096,
153616192, 153747008, 153878336, 154008256, 154139968, 154270912,
154402624, 154533824, 154663616, 154795712, 154926272, 155057984,
155188928, 155319872, 155450816, 155580608, 155712064, 155843392,
155971136, 156106688, 156237376, 156367424, 156499264, 156630976,
156761536, 156892352, 157024064, 157155008, 157284416, 157415872,
157545536, 157677248, 157810496, 157938112, 158071744, 158203328,
158334656, 158464832, 158596288, 158727616, 158858048, 158988992,
159121216, 159252416, 159381568, 159513152, 159645632, 159776192,
159906496, 160038464, 160169536, 160300352, 160430656, 160563008,
160693952, 160822208, 160956352, 161086784, 161217344, 161349184,
161480512, 161611456, 161742272, 161873216, 162002752, 162135872,
162266432, 162397888, 162529216, 162660032, 162790976, 162922048,
163052096, 163184576, 163314752, 163446592, 163577408, 163707968,
163839296, 163969984, 164100928, 164233024, 164364224, 164494912,
164625856, 164756672, 164887616, 165019072, 165150016, 165280064,
165412672, 165543104, 165674944, 165805888, 165936832, 166067648,
166198336, 166330048, 166461248, 166591552, 166722496, 166854208,
166985408, 167116736, 167246656, 167378368, 167508416, 167641024,
167771584, 167903168, 168034112, 168164032, 168295744, 168427456,
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Last updated