Home/Chain Registry/Block #41,487

Block #41,487

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/14/2013, 4:44:22 PM · Difficulty 8.5287 · 6,748,184 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

121eb5cd7d0785b827366a052d07dd5d04de02793a530e49a660d8c7ec124b13

View on Chainz ↗

Height

#41,487

Difficulty

8.528681

Transactions

Size

199 B

Version

Bits

0887579d

Nonce

Timestamp

7/14/2013, 4:44:22 PM

Confirmations

6,748,184

Merkle Root

e84afca34dbf8e1435c1d2eabf1e03e8571dfcd327b4a53211eb76387447e7e5

Transactions (1)

Coinbasee84afca34dbf8e…eb76387447e7e5

1 in → 1 out13.7300 XPM110 B

AWbkF1ZG…vJe1FZPp

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.

2.293 × 10⁹¹(92-digit number)

22935831472964149530…96777267558765851190

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

2.293 × 10⁹¹(92-digit number)

22935831472964149530…96777267558765851191

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.587 × 10⁹¹(92-digit number)

45871662945928299060…93554535117531702381

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.174 × 10⁹¹(92-digit number)

91743325891856598120…87109070235063404761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.834 × 10⁹²(93-digit number)

18348665178371319624…74218140470126809521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.669 × 10⁹²(93-digit number)

36697330356742639248…48436280940253619041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.339 × 10⁹²(93-digit number)

73394660713485278496…96872561880507238081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.467 × 10⁹³(94-digit number)

14678932142697055699…93745123761014476161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.935 × 10⁹³(94-digit number)

29357864285394111398…87490247522028952321

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 41487

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 121eb5cd7d0785b827366a052d07dd5d04de02793a530e49a660d8c7ec124b13

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 #41,487 on Chainz ↗