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Block #237,371

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/1/2013, 12:28:13 AM Β· Difficulty 9.9495 Β· 6,575,245 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ec82ae2fc87aea2bf3a6fe1677792924c919b07284e9f3c99e53b94761907c7e
View on Chainz β†—

Height

#237,371

Difficulty

9.949534

Transactions

1

Size

206 B

Version

2

Bits

09f314ab

Nonce

33,555,213

Timestamp

11/1/2013, 12:28:13 AM

Confirmations

6,575,245

Merkle Root

0a2ab5bd4cbba6da769dad1ccf2d9fc6baa476077cfa00a9789e866834eb1e90
Transactions (1)
Coinbase0a2ab5bd4cbba6…9e866834eb1e90
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.

5.548 Γ— 10⁹⁴(95-digit number)
55482172710680931440…50980118312145600000
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
5.548 Γ— 10⁹⁴(95-digit number)
55482172710680931440…50980118312145600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.109 Γ— 10⁹⁡(96-digit number)
11096434542136186288…01960236624291200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.219 Γ— 10⁹⁡(96-digit number)
22192869084272372576…03920473248582400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.438 Γ— 10⁹⁡(96-digit number)
44385738168544745152…07840946497164800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.877 Γ— 10⁹⁡(96-digit number)
88771476337089490304…15681892994329600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.775 Γ— 10⁹⁢(97-digit number)
17754295267417898060…31363785988659200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.550 Γ— 10⁹⁢(97-digit number)
35508590534835796121…62727571977318400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.101 Γ— 10⁹⁢(97-digit number)
71017181069671592243…25455143954636800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.420 Γ— 10⁹⁷(98-digit number)
14203436213934318448…50910287909273600001
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 237371

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 ec82ae2fc87aea2bf3a6fe1677792924c919b07284e9f3c99e53b94761907c7e

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 #237,371 on Chainz β†—
Circulating Supply:57,744,966 XPMΒ·at block #6,812,615 Β· updates every 60s
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