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Block #52,129

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 8:57:48 AM Β· Difficulty 8.9081 Β· 6,760,243 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
23a2d24dd81cb4e77f44f042cdfb3a65d79db329e744853f45fa1bef3b629627
View on Chainz β†—

Height

#52,129

Difficulty

8.908074

Transactions

2

Size

472 B

Version

2

Bits

08e87782

Nonce

402

Timestamp

7/16/2013, 8:57:48 AM

Confirmations

6,760,243

Merkle Root

4f963baaa23ad36ceeb6c9fe26df7ae021551f6faacef57a88dfa02dd60a27ab
Transactions (2)
Coinbase45a6a0d13fa0d3…3b8cfd1828d269
1 in β†’ 1 out12.5900 XPM110 B
AW52L9ui…216HJvuH
f592d23a98804d…df9b234f698baa
2 in β†’ 1 out36.5400 XPM271 B
AZYmHKof…V5dQJr86
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.

2.905 Γ— 10⁹⁢(97-digit number)
29051058352318236272…87457903456840439180
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
2.905 Γ— 10⁹⁢(97-digit number)
29051058352318236272…87457903456840439181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.810 Γ— 10⁹⁢(97-digit number)
58102116704636472545…74915806913680878361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.162 Γ— 10⁹⁷(98-digit number)
11620423340927294509…49831613827361756721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.324 Γ— 10⁹⁷(98-digit number)
23240846681854589018…99663227654723513441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.648 Γ— 10⁹⁷(98-digit number)
46481693363709178036…99326455309447026881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.296 Γ— 10⁹⁷(98-digit number)
92963386727418356072…98652910618894053761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.859 Γ— 10⁹⁸(99-digit number)
18592677345483671214…97305821237788107521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.718 Γ— 10⁹⁸(99-digit number)
37185354690967342428…94611642475576215041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 52129

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 23a2d24dd81cb4e77f44f042cdfb3a65d79db329e744853f45fa1bef3b629627

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 #52,129 on Chainz β†—
Circulating Supply:57,742,997 XPMΒ·at block #6,812,371 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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