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Block #3,864

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/9/2013, 8:08:33 AM · Difficulty 7.2734 · 6,785,776 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c33ed9ae0175d6c905b43cc9e9b7d6e6d1bc7a049e3413f87480eb0c4f801122

View on Chainz ↗

Height

#3,864

Difficulty

7.273433

Transactions

Size

204 B

Version

Bits

0745ffb1

Nonce

Timestamp

7/9/2013, 8:08:33 AM

Confirmations

6,785,776

Merkle Root

05d961ca782abd1ce68445a0aece3bc5a4abe3b915cda349f0aa09ea4d872b93

Transactions (1)

Coinbase05d961ca782abd…aa09ea4d872b93

1 in → 1 out18.8800 XPM108 B

AG2KbaFX…wSGtDv2R

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.

5.616 × 10¹⁰⁸(109-digit number)

56166298868721270427…78739221444430650240

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

5.616 × 10¹⁰⁸(109-digit number)

56166298868721270427…78739221444430650241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.123 × 10¹⁰⁹(110-digit number)

11233259773744254085…57478442888861300481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.246 × 10¹⁰⁹(110-digit number)

22466519547488508170…14956885777722600961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.493 × 10¹⁰⁹(110-digit number)

44933039094977016341…29913771555445201921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.986 × 10¹⁰⁹(110-digit number)

89866078189954032683…59827543110890403841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.797 × 10¹¹⁰(111-digit number)

17973215637990806536…19655086221780807681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.594 × 10¹¹⁰(111-digit number)

35946431275981613073…39310172443561615361

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 3864

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 c33ed9ae0175d6c905b43cc9e9b7d6e6d1bc7a049e3413f87480eb0c4f801122

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 #3,864 on Chainz ↗