Home/Chain Registry/Block #208,281

Block #208,281

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/13/2013, 10:26:38 PM · Difficulty 9.9056 · 6,616,788 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ea860585a06cb65fd6b4ff4617e7378140aa144ba8d56c4ea617d0586fbb0903

View on Chainz ↗

Height

#208,281

Difficulty

9.905583

Transactions

Size

1.07 KB

Version

Bits

09e7d44e

Nonce

153,943

Timestamp

10/13/2013, 10:26:38 PM

Confirmations

6,616,788

Merkle Root

4eb894daedc2bae9cf38abc3f5da48a187c2a31c4f7d1a67e4305c73419a4945

Transactions (3)

Coinbasea4cef456c6524f…cb70b99744fd7a

1 in → 1 out10.2500 XPM109 B

AeRvqbyP…QbG5TNLq

6eb57b5fa1425b…6dfa942d01e79a

4 in → 2 out299.9097 XPM673 B

AWAxsoSt…j9FoMT2m AaYjzXKJ…jacAgxc1

160b739b0d6512…b58924df20d17f

1 in → 2 out226.4458 XPM226 B

AKRkbogZ…Zcr5oafo AT9UKey3…5pJFehS8

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.

4.029 × 10⁹³(94-digit number)

40295089084169196032…33319269178061269420

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

4.029 × 10⁹³(94-digit number)

40295089084169196032…33319269178061269421

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.059 × 10⁹³(94-digit number)

80590178168338392064…66638538356122538841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.611 × 10⁹⁴(95-digit number)

16118035633667678412…33277076712245077681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.223 × 10⁹⁴(95-digit number)

32236071267335356825…66554153424490155361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.447 × 10⁹⁴(95-digit number)

64472142534670713651…33108306848980310721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.289 × 10⁹⁵(96-digit number)

12894428506934142730…66216613697960621441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.578 × 10⁹⁵(96-digit number)

25788857013868285460…32433227395921242881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.157 × 10⁹⁵(96-digit number)

51577714027736570921…64866454791842485761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.031 × 10⁹⁶(97-digit number)

10315542805547314184…29732909583684971521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.063 × 10⁹⁶(97-digit number)

20631085611094628368…59465819167369943041

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 208281

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 ea860585a06cb65fd6b4ff4617e7378140aa144ba8d56c4ea617d0586fbb0903

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 #208,281 on Chainz ↗

Block #208,281

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