Home/Chain Registry/Block #339,804

Block #339,804

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/2/2014, 8:36:38 AM · Difficulty 10.1301 · 6,465,828 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

bbc96959a44853d56b6d5dfe31899db79efaab071de5f8231bcb4561ae3d8d54

View on Chainz ↗

Height

#339,804

Difficulty

10.130143

Transactions

Size

1.08 KB

Version

Bits

0a215112

Nonce

194,466

Timestamp

1/2/2014, 8:36:38 AM

Confirmations

6,465,828

Merkle Root

cdc7512b5738f51778e50dbaf4f9692e98f23edc887810eb43f17b17d238c5f3

Transactions (1)

Coinbasecdc7512b5738f5…f17b17d238c5f3

1 in → 28 out9.7100 XPM1015 B

AYF7M7hn…ZSUxv1aS APeshfYV…3PKcKMKH AQ8QAT3J…rCFKuVbR AQwv1sMK…D8hyuJxu AKFpswQy…X9UZms87

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.

1.085 × 10⁹⁹(100-digit number)

10853748025118086913…76304581201230940160

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

1.085 × 10⁹⁹(100-digit number)

10853748025118086913…76304581201230940161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.170 × 10⁹⁹(100-digit number)

21707496050236173827…52609162402461880321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.341 × 10⁹⁹(100-digit number)

43414992100472347654…05218324804923760641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.682 × 10⁹⁹(100-digit number)

86829984200944695308…10436649609847521281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.736 × 10¹⁰⁰(101-digit number)

17365996840188939061…20873299219695042561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.473 × 10¹⁰⁰(101-digit number)

34731993680377878123…41746598439390085121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.946 × 10¹⁰⁰(101-digit number)

69463987360755756247…83493196878780170241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.389 × 10¹⁰¹(102-digit number)

13892797472151151249…66986393757560340481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.778 × 10¹⁰¹(102-digit number)

27785594944302302498…33972787515120680961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.557 × 10¹⁰¹(102-digit number)

55571189888604604997…67945575030241361921

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 339804

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 bbc96959a44853d56b6d5dfe31899db79efaab071de5f8231bcb4561ae3d8d54

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 #339,804 on Chainz ↗