Home/Chain Registry/Block #356,825

Block #356,825

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/13/2014, 12:07:59 AM · Difficulty 10.3823 · 6,448,547 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2197446d8fe7734e6aaa3dd2a5d15042f0a5fecd182f7db21e793c770d904279

View on Chainz ↗

Height

#356,825

Difficulty

10.382307

Transactions

Size

209 B

Version

Bits

0a61dee3

Nonce

26,666

Timestamp

1/13/2014, 12:07:59 AM

Confirmations

6,448,547

Merkle Root

76c006cdb66d581a1bb36efa72f0e190416a19b24eed5e17037d308f407fd50c

Transactions (1)

Coinbase76c006cdb66d58…7d308f407fd50c

1 in → 1 out9.2600 XPM116 B

AbwWkWZt…kawDhufa

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.

9.428 × 10¹⁰⁰(101-digit number)

94283387233400083055…19799461234892228480

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

9.428 × 10¹⁰⁰(101-digit number)

94283387233400083055…19799461234892228481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.885 × 10¹⁰¹(102-digit number)

18856677446680016611…39598922469784456961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.771 × 10¹⁰¹(102-digit number)

37713354893360033222…79197844939568913921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.542 × 10¹⁰¹(102-digit number)

75426709786720066444…58395689879137827841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.508 × 10¹⁰²(103-digit number)

15085341957344013288…16791379758275655681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.017 × 10¹⁰²(103-digit number)

30170683914688026577…33582759516551311361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.034 × 10¹⁰²(103-digit number)

60341367829376053155…67165519033102622721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.206 × 10¹⁰³(104-digit number)

12068273565875210631…34331038066205245441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.413 × 10¹⁰³(104-digit number)

24136547131750421262…68662076132410490881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.827 × 10¹⁰³(104-digit number)

48273094263500842524…37324152264820981761

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 356825

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 2197446d8fe7734e6aaa3dd2a5d15042f0a5fecd182f7db21e793c770d904279

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 #356,825 on Chainz ↗