Home/Chain Registry/Block #356,922

Block #356,922

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/13/2014, 1:40:14 AM · Difficulty 10.3826 · 6,458,099 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

31a37a28cf06e979d99179ec088d4dca39bd6cfe6da0c91e6f85dc46e122f435

View on Chainz ↗

Height

#356,922

Difficulty

10.382555

Transactions

Size

879 B

Version

Bits

0a61ef1a

Nonce

7,167

Timestamp

1/13/2014, 1:40:14 AM

Confirmations

6,458,099

Merkle Root

e52a67398e5b35a0cb5e5975b56a5889efac4f0e4c033ab48da916485e65515c

Transactions (4)

Coinbase0728331cab7aae…8ec0b45940a00d

1 in → 1 out9.2900 XPM109 B

AFq7Ptso…8GXuZDEH

d9452861c61ba1…cfb66aa9a545f4

1 in → 2 out7.3284 XPM226 B

Ab4DqPHA…V2gWPd5w AHDArqQW…nNZMgWAb

a3442d0ec28383…e708fd50c62e62

1 in → 2 out7.3030 XPM226 B

AJtuJqkd…aNDvMbiC AcMGrAri…B2TuD6Vy

11bded5426ef22…6029e383821794

1 in → 2 out6.2813 XPM226 B

AQEkERhm…8qHtT9E8 ARd47WCo…vXzjgLiX

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.

4.829 × 10⁹⁹(100-digit number)

48291080927409388584…73306486029378362560

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

4.829 × 10⁹⁹(100-digit number)

48291080927409388584…73306486029378362561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.658 × 10⁹⁹(100-digit number)

96582161854818777169…46612972058756725121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.931 × 10¹⁰⁰(101-digit number)

19316432370963755433…93225944117513450241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.863 × 10¹⁰⁰(101-digit number)

38632864741927510867…86451888235026900481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.726 × 10¹⁰⁰(101-digit number)

77265729483855021735…72903776470053800961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.545 × 10¹⁰¹(102-digit number)

15453145896771004347…45807552940107601921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.090 × 10¹⁰¹(102-digit number)

30906291793542008694…91615105880215203841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.181 × 10¹⁰¹(102-digit number)

61812583587084017388…83230211760430407681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.236 × 10¹⁰²(103-digit number)

12362516717416803477…66460423520860815361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.472 × 10¹⁰²(103-digit number)

24725033434833606955…32920847041721630721

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 356922

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 31a37a28cf06e979d99179ec088d4dca39bd6cfe6da0c91e6f85dc46e122f435

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 #356,922 on Chainz ↗

Block #356,922

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