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Home/Chain Registry/Block #2,854,266

Block #2,854,266

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 9/25/2018, 7:06:47 AM Β· Difficulty 11.7099 Β· 3,987,987 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
e323b1e3454df55836014e28d4cb60218a202264b776616acdda3817604310a4
View on Chainz β†—

Difficulty

11.709922

Transactions

1

Size

201 B

Version

2

Bits

0bb5bd78

Nonce

617,186,778

Timestamp

9/25/2018, 7:06:47 AM

Confirmations

3,987,987

Merkle Root

b10c7dbb68fc97607961352ec5089500da27ed49c80f88e9da5cb167d9ab544a
Transactions (1)
Coinbaseb10c7dbb68fc97…5cb167d9ab544a
1 in β†’ 1 out7.2800 XPM110 B
Ae9hWQ6T…FyWF6Cb2
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.628 Γ— 10⁹⁢(97-digit number)
16285002014701508625…70730807823148910080
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
1.628 Γ— 10⁹⁢(97-digit number)
16285002014701508625…70730807823148910079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.257 Γ— 10⁹⁢(97-digit number)
32570004029403017251…41461615646297820159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.514 Γ— 10⁹⁢(97-digit number)
65140008058806034503…82923231292595640319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.302 Γ— 10⁹⁷(98-digit number)
13028001611761206900…65846462585191280639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.605 Γ— 10⁹⁷(98-digit number)
26056003223522413801…31692925170382561279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.211 Γ— 10⁹⁷(98-digit number)
52112006447044827603…63385850340765122559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.042 Γ— 10⁹⁸(99-digit number)
10422401289408965520…26771700681530245119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.084 Γ— 10⁹⁸(99-digit number)
20844802578817931041…53543401363060490239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.168 Γ— 10⁹⁸(99-digit number)
41689605157635862082…07086802726120980479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.337 Γ— 10⁹⁸(99-digit number)
83379210315271724164…14173605452241960959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.667 Γ— 10⁹⁹(100-digit number)
16675842063054344832…28347210904483921919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
3.335 Γ— 10⁹⁹(100-digit number)
33351684126108689665…56694421808967843839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2854266

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock e323b1e3454df55836014e28d4cb60218a202264b776616acdda3817604310a4

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,854,266 on Chainz β†—
Circulating Supply:57,982,421 XPMΒ·at block #6,842,252 Β· updates every 60s
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