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Home/Chain Registry/Block #2,647,380

Block #2,647,380

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 9:43:39 PM Β· Difficulty 11.7585 Β· 4,191,051 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
89e581a3c4a96cf944379251deeab4bc1e49e054b76538f8d2d0027114449d92
View on Chainz β†—

Difficulty

11.758500

Transactions

1

Size

201 B

Version

2

Bits

0bc22d15

Nonce

1,142,691,192

Timestamp

5/3/2018, 9:43:39 PM

Confirmations

4,191,051

Merkle Root

c29cd0da2e5b1cb60e39b8fdcdb09ef92573dd4ff97c1d5d755420774f3499a8
Transactions (1)
Coinbasec29cd0da2e5b1c…5420774f3499a8
1 in β†’ 1 out7.2200 XPM110 B
AdBxniUs…2mpc79LK
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.

1.416 Γ— 10⁹⁷(98-digit number)
14163121187854550398…76030418435281715200
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
1.416 Γ— 10⁹⁷(98-digit number)
14163121187854550398…76030418435281715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.832 Γ— 10⁹⁷(98-digit number)
28326242375709100797…52060836870563430401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.665 Γ— 10⁹⁷(98-digit number)
56652484751418201594…04121673741126860801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.133 Γ— 10⁹⁸(99-digit number)
11330496950283640318…08243347482253721601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.266 Γ— 10⁹⁸(99-digit number)
22660993900567280637…16486694964507443201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.532 Γ— 10⁹⁸(99-digit number)
45321987801134561275…32973389929014886401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.064 Γ— 10⁹⁸(99-digit number)
90643975602269122551…65946779858029772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.812 Γ— 10⁹⁹(100-digit number)
18128795120453824510…31893559716059545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.625 Γ— 10⁹⁹(100-digit number)
36257590240907649020…63787119432119091201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.251 Γ— 10⁹⁹(100-digit number)
72515180481815298041…27574238864238182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.450 Γ— 10¹⁰⁰(101-digit number)
14503036096363059608…55148477728476364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.900 Γ— 10¹⁰⁰(101-digit number)
29006072192726119216…10296955456952729601
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 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
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 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 2647380

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 89e581a3c4a96cf944379251deeab4bc1e49e054b76538f8d2d0027114449d92

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 #2,647,380 on Chainz β†—
Circulating Supply:57,951,723 XPMΒ·at block #6,838,430 Β· updates every 60s
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