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Block #544,694

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/15/2014, 12:31:22 AM Β· Difficulty 10.9513 Β· 6,279,911 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9c8d9152a1b381a49646ab22be8f4e15c3753077cf29145893df8edceb97bfe2
View on Chainz β†—

Height

#544,694

Difficulty

10.951307

Transactions

1

Size

208 B

Version

2

Bits

0af388d5

Nonce

1,155,005,115

Timestamp

5/15/2014, 12:31:22 AM

Confirmations

6,279,911

Merkle Root

3a3ea6280238170705eae06ad13d1fb7efb9bfae22c46dbe5d29827dab41a5a0
Transactions (1)
Coinbase3a3ea628023817…29827dab41a5a0
1 in β†’ 1 out8.3200 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.

2.526 Γ— 10¹⁰⁰(101-digit number)
25261470061934575522…88208637211326208000
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
2.526 Γ— 10¹⁰⁰(101-digit number)
25261470061934575522…88208637211326208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.052 Γ— 10¹⁰⁰(101-digit number)
50522940123869151044…76417274422652416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.010 Γ— 10¹⁰¹(102-digit number)
10104588024773830208…52834548845304832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.020 Γ— 10¹⁰¹(102-digit number)
20209176049547660417…05669097690609664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.041 Γ— 10¹⁰¹(102-digit number)
40418352099095320835…11338195381219328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.083 Γ— 10¹⁰¹(102-digit number)
80836704198190641671…22676390762438656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.616 Γ— 10¹⁰²(103-digit number)
16167340839638128334…45352781524877312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.233 Γ— 10¹⁰²(103-digit number)
32334681679276256668…90705563049754624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.466 Γ— 10¹⁰²(103-digit number)
64669363358552513337…81411126099509248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.293 Γ— 10¹⁰³(104-digit number)
12933872671710502667…62822252199018496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.586 Γ— 10¹⁰³(104-digit number)
25867745343421005334…25644504398036992001
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 544694

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 9c8d9152a1b381a49646ab22be8f4e15c3753077cf29145893df8edceb97bfe2

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 #544,694 on Chainz β†—
Circulating Supply:57,840,910 XPMΒ·at block #6,824,604 Β· updates every 60s
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