Home/Chain Registry/Block #387,862

Block #387,862

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/3/2014, 10:11:20 AM · Difficulty 10.4156 · 6,451,803 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

cc1224b19cbd86342a040be97af14067fb45d167c79042177079091bde698785

View on Chainz ↗

Height

#387,862

Difficulty

10.415592

Transactions

Size

1.44 KB

Version

Bits

0a6a643a

Nonce

4,466

Timestamp

2/3/2014, 10:11:20 AM

Confirmations

6,451,803

Merkle Root

6fb1bbf2a3ce0371d36e12a16694a6ed11ae309d3a3c1975d319ee87a6c50840

Transactions (4)

Coinbase697e5731dae308…e13bea95329d6f

1 in → 20 out9.2000 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6 Ab9NZWSq…3UkdcwAB

6c459cec294b7c…237d936d68292a

1 in → 1 out3.0000 XPM193 B

AY17Hcid…N4rcNxmD

8615baea943cba…b79977a531466f

1 in → 2 out5.1365 XPM226 B

ALMptXJJ…6SedJYh6 AXxp24rY…yi3yUFBu

490d549744b038…b9bd2beb12eea5

1 in → 2 out4.8392 XPM225 B

AP54Esp3…agcTfHb3 AdpsxmtJ…ZWfmvRK9

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.

5.590 × 10⁹⁰(91-digit number)

55903654666704264022…39684816327642773150

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

5.590 × 10⁹⁰(91-digit number)

55903654666704264022…39684816327642773151

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.118 × 10⁹¹(92-digit number)

11180730933340852804…79369632655285546301

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.236 × 10⁹¹(92-digit number)

22361461866681705608…58739265310571092601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.472 × 10⁹¹(92-digit number)

44722923733363411217…17478530621142185201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.944 × 10⁹¹(92-digit number)

89445847466726822435…34957061242284370401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.788 × 10⁹²(93-digit number)

17889169493345364487…69914122484568740801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.577 × 10⁹²(93-digit number)

35778338986690728974…39828244969137481601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.155 × 10⁹²(93-digit number)

71556677973381457948…79656489938274963201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.431 × 10⁹³(94-digit number)

14311335594676291589…59312979876549926401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.862 × 10⁹³(94-digit number)

28622671189352583179…18625959753099852801

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 387862

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 cc1224b19cbd86342a040be97af14067fb45d167c79042177079091bde698785

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 #387,862 on Chainz ↗

Block #387,862

Cookie Preferences