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Block #565,521

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/28/2014, 8:50:08 AM · Difficulty 10.9652 · 6,260,644 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

36c138ce12745cd25c75ab615f76d9b8320c08b939bfba1dff24ce6abb9289d5

View on Chainz ↗

Height

#565,521

Difficulty

10.965221

Transactions

Size

207 B

Version

Bits

0af718b3

Nonce

1,284,148,966

Timestamp

5/28/2014, 8:50:08 AM

Confirmations

6,260,644

Merkle Root

a63660dc2b60c454c19afd452b66e850aedc3bc16bca86bb706bbd45104775d1

Transactions (1)

Coinbasea63660dc2b60c4…6bbd45104775d1

1 in → 1 out8.3000 XPM116 B

ANSXnLY2…Sd25TjkD

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.

1.595 × 10⁹⁸(99-digit number)

15959838401257823980…00128361243551245260

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

1.595 × 10⁹⁸(99-digit number)

15959838401257823980…00128361243551245261

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.191 × 10⁹⁸(99-digit number)

31919676802515647961…00256722487102490521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.383 × 10⁹⁸(99-digit number)

63839353605031295922…00513444974204981041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.276 × 10⁹⁹(100-digit number)

12767870721006259184…01026889948409962081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.553 × 10⁹⁹(100-digit number)

25535741442012518369…02053779896819924161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.107 × 10⁹⁹(100-digit number)

51071482884025036738…04107559793639848321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.021 × 10¹⁰⁰(101-digit number)

10214296576805007347…08215119587279696641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.042 × 10¹⁰⁰(101-digit number)

20428593153610014695…16430239174559393281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.085 × 10¹⁰⁰(101-digit number)

40857186307220029390…32860478349118786561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.171 × 10¹⁰⁰(101-digit number)

81714372614440058781…65720956698237573121

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 565521

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 36c138ce12745cd25c75ab615f76d9b8320c08b939bfba1dff24ce6abb9289d5

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 #565,521 on Chainz ↗

Block #565,521

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