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Block #589,552

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/15/2014, 1:50:00 PM Β· Difficulty 10.9474 Β· 6,222,822 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b6647b62cddc96aa05c1ec88518282dc8e127b014ed4e8397a1806a18c2861b
View on Chainz β†—

Height

#589,552

Difficulty

10.947426

Transactions

1

Size

207 B

Version

2

Bits

0af28a86

Nonce

206,393,711

Timestamp

6/15/2014, 1:50:00 PM

Confirmations

6,222,822

Merkle Root

c64cdbdef5bba8a063e4459abda86ecf57e97e7a7dfcc53b320fa6a1bc5b09c2
Transactions (1)
Coinbasec64cdbdef5bba8…0fa6a1bc5b09c2
1 in β†’ 1 out8.3300 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.

8.221 Γ— 10⁹⁢(97-digit number)
82218703531209516858…02623417345895175800
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
8.221 Γ— 10⁹⁢(97-digit number)
82218703531209516858…02623417345895175801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.644 Γ— 10⁹⁷(98-digit number)
16443740706241903371…05246834691790351601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.288 Γ— 10⁹⁷(98-digit number)
32887481412483806743…10493669383580703201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.577 Γ— 10⁹⁷(98-digit number)
65774962824967613487…20987338767161406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.315 Γ— 10⁹⁸(99-digit number)
13154992564993522697…41974677534322812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.630 Γ— 10⁹⁸(99-digit number)
26309985129987045394…83949355068645625601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.261 Γ— 10⁹⁸(99-digit number)
52619970259974090789…67898710137291251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.052 Γ— 10⁹⁹(100-digit number)
10523994051994818157…35797420274582502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.104 Γ— 10⁹⁹(100-digit number)
21047988103989636315…71594840549165004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.209 Γ— 10⁹⁹(100-digit number)
42095976207979272631…43189681098330009601
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 589552

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 2b6647b62cddc96aa05c1ec88518282dc8e127b014ed4e8397a1806a18c2861b

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 #589,552 on Chainz β†—
Circulating Supply:57,743,013 XPMΒ·at block #6,812,373 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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