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Home/Chain Registry/Block #2,551,181

Block #2,551,181

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/6/2018, 3:15:19 AM Β· Difficulty 10.9893 Β· 4,291,939 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7a220656b294e12091f11dc31b98c72e4758c1c3f7b8d41fd172c27368467b5d
View on Chainz β†—

Difficulty

10.989259

Transactions

1

Size

200 B

Version

2

Bits

0afd401c

Nonce

71,544,496

Timestamp

3/6/2018, 3:15:19 AM

Confirmations

4,291,939

Merkle Root

9dd9ebffd215375597d0223709db97eac8a834fe61bdd6c9196b556a0d561dd6
Transactions (1)
Coinbase9dd9ebffd21537…6b556a0d561dd6
1 in β†’ 1 out8.2700 XPM110 B
ATas56V5…bQArSboW
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.

2.291 Γ— 10⁹⁡(96-digit number)
22915125774401205309…56279815685034127040
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.291 Γ— 10⁹⁡(96-digit number)
22915125774401205309…56279815685034127041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.583 Γ— 10⁹⁡(96-digit number)
45830251548802410618…12559631370068254081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.166 Γ— 10⁹⁡(96-digit number)
91660503097604821236…25119262740136508161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.833 Γ— 10⁹⁢(97-digit number)
18332100619520964247…50238525480273016321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.666 Γ— 10⁹⁢(97-digit number)
36664201239041928494…00477050960546032641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.332 Γ— 10⁹⁢(97-digit number)
73328402478083856989…00954101921092065281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.466 Γ— 10⁹⁷(98-digit number)
14665680495616771397…01908203842184130561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.933 Γ— 10⁹⁷(98-digit number)
29331360991233542795…03816407684368261121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.866 Γ— 10⁹⁷(98-digit number)
58662721982467085591…07632815368736522241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.173 Γ— 10⁹⁸(99-digit number)
11732544396493417118…15265630737473044481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.346 Γ— 10⁹⁸(99-digit number)
23465088792986834236…30531261474946088961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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
RareChain length 11
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2551181

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 7a220656b294e12091f11dc31b98c72e4758c1c3f7b8d41fd172c27368467b5d

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 #2,551,181 on Chainz β†—
Circulating Supply:57,989,325 XPMΒ·at block #6,843,119 Β· updates every 60s
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