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Block #3,863

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/9/2013, 8:08:05 AM · Difficulty 7.2734 · 6,785,878 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a714b9bc0d6d9b0627996a18cffc8d9737920b9e0ac3a37ca1f7e23791c17b62

View on Chainz ↗

Height

#3,863

Difficulty

7.273351

Transactions

Size

198 B

Version

Bits

0745fa56

Nonce

711

Timestamp

7/9/2013, 8:08:05 AM

Confirmations

6,785,878

Merkle Root

3d1acbe92ca081d24697134108611beba1648080760cbedcc90ee9d0e1f6a92b

Transactions (1)

Coinbase3d1acbe92ca081…0ee9d0e1f6a92b

1 in → 1 out18.8800 XPM108 B

AaMtpsGc…KcnVCSkq

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.

6.067 × 10⁹⁵(96-digit number)

60674668818977412825…62183441237815782240

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

6.067 × 10⁹⁵(96-digit number)

60674668818977412825…62183441237815782241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.213 × 10⁹⁶(97-digit number)

12134933763795482565…24366882475631564481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.426 × 10⁹⁶(97-digit number)

24269867527590965130…48733764951263128961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.853 × 10⁹⁶(97-digit number)

48539735055181930260…97467529902526257921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.707 × 10⁹⁶(97-digit number)

97079470110363860520…94935059805052515841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.941 × 10⁹⁷(98-digit number)

19415894022072772104…89870119610105031681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.883 × 10⁹⁷(98-digit number)

38831788044145544208…79740239220210063361

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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

CommonChain length 7

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 3863

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 a714b9bc0d6d9b0627996a18cffc8d9737920b9e0ac3a37ca1f7e23791c17b62

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 #3,863 on Chainz ↗