Home/Chain Registry/Block #502,057

Block #502,057

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/20/2014, 4:14:55 AM · Difficulty 10.8065 · 6,324,819 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7c2152635316fcc7fce2f0f4aa45b53ff4dcac91e51e343089ef5e4394224993

View on Chainz ↗

Height

#502,057

Difficulty

10.806542

Transactions

Size

887 B

Version

Bits

0ace7986

Nonce

276,944,480

Timestamp

4/20/2014, 4:14:55 AM

Confirmations

6,324,819

Merkle Root

d83982141d76d2b04da2ed3d3f1166951a553451f5e255ff99d5f5f13d759f61

Transactions (4)

Coinbase686cec1ed73168…f8931af08e328e

1 in → 1 out8.5800 XPM116 B

AbwWkWZt…kawDhufa

b90f46d33aa936…5b78267aff5aca

1 in → 2 out8.5800 XPM227 B

AUNRQTBn…oS9zhjJw AbsYMfb4…LWD6uvgS

3103df7cebc320…2d94a60b42a9db

1 in → 2 out8.5800 XPM225 B

AUgtVtbi…qqMqaYu7 AWNxrN85…LMsAYrUp

fcadd3f019607d…24a65fb9fe7801

1 in → 2 out0.7622 XPM227 B

ARRoiuen…7VFFtwSX AWBYeKuV…6a4dkdQu

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.

1.362 × 10¹⁰⁰(101-digit number)

13622672950352251934…82858667345205176320

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

1.362 × 10¹⁰⁰(101-digit number)

13622672950352251934…82858667345205176321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.724 × 10¹⁰⁰(101-digit number)

27245345900704503868…65717334690410352641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.449 × 10¹⁰⁰(101-digit number)

54490691801409007736…31434669380820705281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.089 × 10¹⁰¹(102-digit number)

10898138360281801547…62869338761641410561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.179 × 10¹⁰¹(102-digit number)

21796276720563603094…25738677523282821121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.359 × 10¹⁰¹(102-digit number)

43592553441127206189…51477355046565642241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.718 × 10¹⁰¹(102-digit number)

87185106882254412378…02954710093131284481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.743 × 10¹⁰²(103-digit number)

17437021376450882475…05909420186262568961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.487 × 10¹⁰²(103-digit number)

34874042752901764951…11818840372525137921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.974 × 10¹⁰²(103-digit number)

69748085505803529902…23637680745050275841

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 502057

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 7c2152635316fcc7fce2f0f4aa45b53ff4dcac91e51e343089ef5e4394224993

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 #502,057 on Chainz ↗

Block #502,057

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