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Block #29,817

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 4:50:42 PM · Difficulty 7.9855 · 6,770,489 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4b9737e820e5287193e32ad34fbb975d20dfc62fccb99bbfff9168d47a94424b

View on Chainz ↗

Height

#29,817

Difficulty

7.985522

Transactions

Size

201 B

Version

Bits

07fc4b32

Nonce

Timestamp

7/13/2013, 4:50:42 PM

Confirmations

6,770,489

Merkle Root

b648ad17b1b9565651ce654472344e3cba2f29347006079c29722dcdc76245ee

Transactions (1)

Coinbaseb648ad17b1b956…722dcdc76245ee

1 in → 1 out15.6600 XPM108 B

ASxnQUdC…ZWp83kYh

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.

9.714 × 10¹⁰⁰(101-digit number)

97144689271881015682…59626035071916264480

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

9.714 × 10¹⁰⁰(101-digit number)

97144689271881015682…59626035071916264481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.942 × 10¹⁰¹(102-digit number)

19428937854376203136…19252070143832528961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.885 × 10¹⁰¹(102-digit number)

38857875708752406273…38504140287665057921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.771 × 10¹⁰¹(102-digit number)

77715751417504812546…77008280575330115841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.554 × 10¹⁰²(103-digit number)

15543150283500962509…54016561150660231681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.108 × 10¹⁰²(103-digit number)

31086300567001925018…08033122301320463361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.217 × 10¹⁰²(103-digit number)

62172601134003850036…16066244602640926721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.243 × 10¹⁰³(104-digit number)

12434520226800770007…32132489205281853441

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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 29817

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 4b9737e820e5287193e32ad34fbb975d20dfc62fccb99bbfff9168d47a94424b

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 #29,817 on Chainz ↗