Home/Chain Registry/Block #26,112

Block #26,112

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 4:20:09 AM · Difficulty 7.9738 · 6,765,472 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3c28bba7a14b3e398382be87410cf49395b7022e482a76a844e5930c83058b05

View on Chainz ↗

Height

#26,112

Difficulty

7.973829

Transactions

Size

203 B

Version

Bits

07f94cda

Nonce

694

Timestamp

7/13/2013, 4:20:09 AM

Confirmations

6,765,472

Merkle Root

26d23ace6da1d71a9969b8937ce75a75cd275c7027f7695b1aa8b26479a54652

Transactions (1)

Coinbase26d23ace6da1d7…a8b26479a54652

1 in → 1 out15.7100 XPM108 B

ANqH1vyR…v8prD56J

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.190 × 10¹⁰⁷(108-digit number)

11901849454067836535…21765974368776329680

Discovered Prime Numbers

p_k = 2^k × 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.

origin + 1

1.190 × 10¹⁰⁷(108-digit number)

11901849454067836535…21765974368776329681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.380 × 10¹⁰⁷(108-digit number)

23803698908135673071…43531948737552659361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.760 × 10¹⁰⁷(108-digit number)

47607397816271346142…87063897475105318721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.521 × 10¹⁰⁷(108-digit number)

95214795632542692285…74127794950210637441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.904 × 10¹⁰⁸(109-digit number)

19042959126508538457…48255589900421274881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.808 × 10¹⁰⁸(109-digit number)

38085918253017076914…96511179800842549761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.617 × 10¹⁰⁸(109-digit number)

76171836506034153828…93022359601685099521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.523 × 10¹⁰⁹(110-digit number)

15234367301206830765…86044719203370199041

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — 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 →

★☆☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 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 26112

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 3c28bba7a14b3e398382be87410cf49395b7022e482a76a844e5930c83058b05

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 → Debug Window → 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 #26,112 on Chainz ↗