Home/Chain Registry/Block #497,196

Block #497,196

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/17/2014, 11:33:55 AM · Difficulty 10.7642 · 6,314,436 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

24295d5af296c7b9239a681f377201ba7c616df633dd750ff7b0a6f01ad52d28

View on Chainz ↗

Height

#497,196

Difficulty

10.764248

Transactions

Size

208 B

Version

Bits

0ac3a5c1

Nonce

570,416,067

Timestamp

4/17/2014, 11:33:55 AM

Confirmations

6,314,436

Merkle Root

313c72a43a77c22427963bf82b79196a8ed64d7251877d20301eb2fd21141001

Transactions (1)

Coinbase313c72a43a77c2…1eb2fd21141001

1 in → 1 out8.6200 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.

5.036 × 10⁹⁹(100-digit number)

50369024567874699292…24029227502118487040

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

5.036 × 10⁹⁹(100-digit number)

50369024567874699292…24029227502118487041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.007 × 10¹⁰⁰(101-digit number)

10073804913574939858…48058455004236974081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.014 × 10¹⁰⁰(101-digit number)

20147609827149879717…96116910008473948161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.029 × 10¹⁰⁰(101-digit number)

40295219654299759434…92233820016947896321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.059 × 10¹⁰⁰(101-digit number)

80590439308599518868…84467640033895792641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.611 × 10¹⁰¹(102-digit number)

16118087861719903773…68935280067791585281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.223 × 10¹⁰¹(102-digit number)

32236175723439807547…37870560135583170561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.447 × 10¹⁰¹(102-digit number)

64472351446879615094…75741120271166341121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.289 × 10¹⁰²(103-digit number)

12894470289375923018…51482240542332682241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.578 × 10¹⁰²(103-digit number)

25788940578751846037…02964481084665364481

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 497196

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 24295d5af296c7b9239a681f377201ba7c616df633dd750ff7b0a6f01ad52d28

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 #497,196 on Chainz ↗

Block #497,196

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