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Block #554,755

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/21/2014, 2:46:32 AM Β· Difficulty 10.9626 Β· 6,262,477 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6493744fa9f0dfd249cdb6c7d6399dbd0e5d841f1424d2bac0e8b33e8cc211e7
View on Chainz β†—

Height

#554,755

Difficulty

10.962577

Transactions

1

Size

208 B

Version

2

Bits

0af66b79

Nonce

584,773,985

Timestamp

5/21/2014, 2:46:32 AM

Confirmations

6,262,477

Merkle Root

9271ad27e3c3a43001e4f1e12f60c8f5532ed2f8e860f03a2eea78d41d92418b
Transactions (1)
Coinbase9271ad27e3c3a4…ea78d41d92418b
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.855 Γ— 10⁹⁹(100-digit number)
28557103887762686167…49099819340313472000
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
2.855 Γ— 10⁹⁹(100-digit number)
28557103887762686167…49099819340313472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.711 Γ— 10⁹⁹(100-digit number)
57114207775525372334…98199638680626944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.142 Γ— 10¹⁰⁰(101-digit number)
11422841555105074466…96399277361253888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.284 Γ— 10¹⁰⁰(101-digit number)
22845683110210148933…92798554722507776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.569 Γ— 10¹⁰⁰(101-digit number)
45691366220420297867…85597109445015552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.138 Γ— 10¹⁰⁰(101-digit number)
91382732440840595735…71194218890031104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.827 Γ— 10¹⁰¹(102-digit number)
18276546488168119147…42388437780062208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.655 Γ— 10¹⁰¹(102-digit number)
36553092976336238294…84776875560124416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.310 Γ— 10¹⁰¹(102-digit number)
73106185952672476588…69553751120248832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.462 Γ— 10¹⁰²(103-digit number)
14621237190534495317…39107502240497664001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 554755

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 6493744fa9f0dfd249cdb6c7d6399dbd0e5d841f1424d2bac0e8b33e8cc211e7

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 #554,755 on Chainz β†—
Circulating Supply:57,781,895 XPMΒ·at block #6,817,231 Β· updates every 60s
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