Home/Chain Registry/Block #364,992

Block #364,992

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/18/2014, 10:59:37 AM · Difficulty 10.4226 · 6,460,611 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ec4a825cd84f3462dea9db07c287ff5e88aa84acc1d84cd6bdd60e7dec151cd8

View on Chainz ↗

Height

#364,992

Difficulty

10.422587

Transactions

Size

1.85 KB

Version

Bits

0a6c2ea2

Nonce

80,927

Timestamp

1/18/2014, 10:59:37 AM

Confirmations

6,460,611

Merkle Root

3e1d80fa80e76634daf42fe10d3025c3a4ba1a6a70e073d0c5f474dafab23cbc

Transactions (4)

Coinbase4e45ee20fdde8b…c2b5a9c4837575

1 in → 27 out9.1900 XPM981 B

AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AYtDvcGs…VuAcA7m7 AKR19pvT…zWLSNpj7

07e34f3d1ee541…f5b70f0344bb24

2 in → 2 out11.4188 XPM372 B

AMo4xYNR…6LV3Le7K AHq8TeVf…Vnx1ZPrz

5b1abac468c77c…019ac457ebfabf

1 in → 2 out4.1334 XPM227 B

AHePCkVF…EwZxBfgT AVd4WUH7…k2PChrXg

4aa3d63abb0c49…b0c1f6a83e028e

1 in → 2 out4.1193 XPM227 B

AUNYVZaS…qArW7Ncd AZcRtoES…zt2WG2bC

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.

3.039 × 10¹⁰⁰(101-digit number)

30394359359948774449…06922819336091209280

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

3.039 × 10¹⁰⁰(101-digit number)

30394359359948774449…06922819336091209281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.078 × 10¹⁰⁰(101-digit number)

60788718719897548898…13845638672182418561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.215 × 10¹⁰¹(102-digit number)

12157743743979509779…27691277344364837121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.431 × 10¹⁰¹(102-digit number)

24315487487959019559…55382554688729674241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.863 × 10¹⁰¹(102-digit number)

48630974975918039118…10765109377459348481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.726 × 10¹⁰¹(102-digit number)

97261949951836078237…21530218754918696961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.945 × 10¹⁰²(103-digit number)

19452389990367215647…43060437509837393921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.890 × 10¹⁰²(103-digit number)

38904779980734431294…86120875019674787841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.780 × 10¹⁰²(103-digit number)

77809559961468862589…72241750039349575681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.556 × 10¹⁰³(104-digit number)

15561911992293772517…44483500078699151361

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 364992

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 ec4a825cd84f3462dea9db07c287ff5e88aa84acc1d84cd6bdd60e7dec151cd8

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 #364,992 on Chainz ↗

Block #364,992

Cookie Preferences