Home/Chain Registry/Block #245,841

Block #245,841

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/5/2013, 5:38:12 PM · Difficulty 9.9641 · 6,554,985 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b9fa4c0a344e674dfd299c85a0e604e3f85b71d7dd5f9983712c8cec0d787587

View on Chainz ↗

Height

#245,841

Difficulty

9.964145

Transactions

Size

1.58 KB

Version

Bits

09f6d23c

Nonce

84,767

Timestamp

11/5/2013, 5:38:12 PM

Confirmations

6,554,985

Merkle Root

4d60f7c1d3b6f518981881ff64bb2fa7c604af450e2ebe9fd310b42d94a32f8f

Transactions (1)

Coinbase4d60f7c1d3b6f5…10b42d94a32f8f

1 in → 43 out10.0400 XPM1.49 KB

Aaf3CsqS…k1Eu3vmJ AQQMyJDA…xUZhKMrK AMbCuLHZ…WSoStwkc APgWZwJ2…1nTrECFn AcEnwywz…vZtt2xTs

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.

2.166 × 10⁹⁵(96-digit number)

21667312985186196338…66060393948065344000

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

2.166 × 10⁹⁵(96-digit number)

21667312985186196338…66060393948065344001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.333 × 10⁹⁵(96-digit number)

43334625970372392677…32120787896130688001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.666 × 10⁹⁵(96-digit number)

86669251940744785355…64241575792261376001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.733 × 10⁹⁶(97-digit number)

17333850388148957071…28483151584522752001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.466 × 10⁹⁶(97-digit number)

34667700776297914142…56966303169045504001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.933 × 10⁹⁶(97-digit number)

69335401552595828284…13932606338091008001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.386 × 10⁹⁷(98-digit number)

13867080310519165656…27865212676182016001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.773 × 10⁹⁷(98-digit number)

27734160621038331313…55730425352364032001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.546 × 10⁹⁷(98-digit number)

55468321242076662627…11460850704728064001

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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 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 × 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 245841

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 b9fa4c0a344e674dfd299c85a0e604e3f85b71d7dd5f9983712c8cec0d787587

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 #245,841 on Chainz ↗