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Block #237,267

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/31/2013, 10:55:15 PM Β· Difficulty 9.9494 Β· 6,587,290 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cead8b18fb18919b05d8032d382959e186951ae8950cb3ecbb4ea29505bef914
View on Chainz β†—

Height

#237,267

Difficulty

9.949421

Transactions

1

Size

206 B

Version

2

Bits

09f30d45

Nonce

2,307

Timestamp

10/31/2013, 10:55:15 PM

Confirmations

6,587,290

Merkle Root

12719d06de596d7880abeee46be8a43281e326da363cd7688771dd9e9816c1e2
Transactions (1)
Coinbase12719d06de596d…71dd9e9816c1e2
1 in β†’ 1 out10.0900 XPM116 B
AcLBm5Z9…S683d7c3
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.

8.605 Γ— 10⁹⁴(95-digit number)
86059001590641352295…73914075126654509840
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
8.605 Γ— 10⁹⁴(95-digit number)
86059001590641352295…73914075126654509841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.721 Γ— 10⁹⁡(96-digit number)
17211800318128270459…47828150253309019681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.442 Γ— 10⁹⁡(96-digit number)
34423600636256540918…95656300506618039361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.884 Γ— 10⁹⁡(96-digit number)
68847201272513081836…91312601013236078721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.376 Γ— 10⁹⁢(97-digit number)
13769440254502616367…82625202026472157441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.753 Γ— 10⁹⁢(97-digit number)
27538880509005232734…65250404052944314881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.507 Γ— 10⁹⁢(97-digit number)
55077761018010465469…30500808105888629761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.101 Γ— 10⁹⁷(98-digit number)
11015552203602093093…61001616211777259521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.203 Γ— 10⁹⁷(98-digit number)
22031104407204186187…22003232423554519041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 237267

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 cead8b18fb18919b05d8032d382959e186951ae8950cb3ecbb4ea29505bef914

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 #237,267 on Chainz β†—
Circulating Supply:57,840,519 XPMΒ·at block #6,824,556 Β· updates every 60s
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