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Block #406,237

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/16/2014, 3:18:08 AM · Difficulty 10.4306 · 6,419,463 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d1c183e946a83af70c8bac8bfcf89084c28b8a46e7a015e6c4336efacedbd843

View on Chainz ↗

Height

#406,237

Difficulty

10.430578

Transactions

Size

1.36 KB

Version

Bits

0a6e3a56

Nonce

4,584

Timestamp

2/16/2014, 3:18:08 AM

Confirmations

6,419,463

Merkle Root

ca505bc52ba08ccb868dd28787849aaffe42013779202a63c37aac066a223f50

Transactions (4)

Coinbase449de2e14b1abc…12681d98331847

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

043afce8e91bbc…1f6c5832096716

1 in → 7 out8.9684 XPM395 B

AHoENRJk…NhmYqijD AVg5YGji…Aq7MMxRC AbaeKB2h…jyjYFUFM AVHcc9zb…JkngbvXL AYmXDTRZ…RjoLiimC

ddca7ec315c6e8…2bc712d62a5eb3

1 in → 7 out5.9690 XPM396 B

AHoENRJk…NhmYqijD AVg5YGji…Aq7MMxRC AVHcc9zb…JkngbvXL AP1o9q3X…Y7U3hv3E AYmXDTRZ…RjoLiimC

c00c0cc45eae2d…1e656b27cdd022

1 in → 7 out5.9688 XPM396 B

AHoENRJk…NhmYqijD AVg5YGji…Aq7MMxRC AVHcc9zb…JkngbvXL AYmXDTRZ…RjoLiimC AGmnuygW…3nbSva41

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.

2.153 × 10¹⁰⁰(101-digit number)

21531443987878202112…18495682902612400000

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

2.153 × 10¹⁰⁰(101-digit number)

21531443987878202112…18495682902612400001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.306 × 10¹⁰⁰(101-digit number)

43062887975756404225…36991365805224800001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.612 × 10¹⁰⁰(101-digit number)

86125775951512808450…73982731610449600001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.722 × 10¹⁰¹(102-digit number)

17225155190302561690…47965463220899200001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.445 × 10¹⁰¹(102-digit number)

34450310380605123380…95930926441798400001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.890 × 10¹⁰¹(102-digit number)

68900620761210246760…91861852883596800001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.378 × 10¹⁰²(103-digit number)

13780124152242049352…83723705767193600001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.756 × 10¹⁰²(103-digit number)

27560248304484098704…67447411534387200001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.512 × 10¹⁰²(103-digit number)

55120496608968197408…34894823068774400001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.102 × 10¹⁰³(104-digit number)

11024099321793639481…69789646137548800001

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 406237

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 d1c183e946a83af70c8bac8bfcf89084c28b8a46e7a015e6c4336efacedbd843

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 #406,237 on Chainz ↗

Block #406,237

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