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Block #52,038

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 8:30:19 AM · Difficulty 8.9069 · 6,743,478 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

49a404afd58298613703b8917d357da1f82a1035c3da2a6d9a412a6ba96b677c

View on Chainz ↗

Height

#52,038

Difficulty

8.906885

Transactions

Size

207 B

Version

Bits

08e8299f

Nonce

2,203

Timestamp

7/16/2013, 8:30:19 AM

Confirmations

6,743,478

Merkle Root

e6d6181ebcb45eac8a8ddbb09ee26cd6c23a806442b47f521367657fd2e7a88c

Transactions (1)

Coinbasee6d6181ebcb45e…67657fd2e7a88c

1 in → 1 out12.5900 XPM110 B

AS2bG86z…Pr6ETY7s

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.

6.157 × 10¹¹⁰(111-digit number)

61578802434110966673…01023701693806183040

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

6.157 × 10¹¹⁰(111-digit number)

61578802434110966673…01023701693806183041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.231 × 10¹¹¹(112-digit number)

12315760486822193334…02047403387612366081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.463 × 10¹¹¹(112-digit number)

24631520973644386669…04094806775224732161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.926 × 10¹¹¹(112-digit number)

49263041947288773338…08189613550449464321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.852 × 10¹¹¹(112-digit number)

98526083894577546677…16379227100898928641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.970 × 10¹¹²(113-digit number)

19705216778915509335…32758454201797857281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.941 × 10¹¹²(113-digit number)

39410433557831018671…65516908403595714561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.882 × 10¹¹²(113-digit number)

78820867115662037342…31033816807191429121

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 52038

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 49a404afd58298613703b8917d357da1f82a1035c3da2a6d9a412a6ba96b677c

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 #52,038 on Chainz ↗