Home/Chain Registry/Block #2,845,289

Block #2,845,289

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/18/2018, 7:52:16 PM · Difficulty 11.7283 · 3,999,609 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b7fe08a4bbd774748a16add83647ae8809fdc9118c6385c13b42e6819393d01d

View on Chainz ↗

Height

#2,845,289

Difficulty

11.728301

Transactions

Size

961 B

Version

Bits

0bba71ed

Nonce

604,216,977

Timestamp

9/18/2018, 7:52:16 PM

Confirmations

3,999,609

Merkle Root

5f33c22ab310c1e9336b41941165a9c19cb3c76973bc46d54c2d9ebdb313beb9

Transactions (4)

Coinbase82fb6df3f9c390…f08740c86d02e6

1 in → 1 out7.2900 XPM110 B

AJwnwDKp…p1yJ65Ba

eda1122c479306…b1702fe8679872

1 in → 2 out7.2500 XPM192 B

AJGtZhZj…1MrK7CBm AdGFnV3a…o6n2zX3x

8729c7c4469352…703895c786b1be

1 in → 2 out7.2500 XPM193 B

AXSDamw3…ZLdH1Ufx AcPP3dDg…AnRLRgfD

829d339f1fe2ae…ad291c9809f036

2 in → 2 out1.0417 XPM375 B

AR13dYFu…SeCGnUVg ARMFdT2w…TGxHik4a

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.

2.105 × 10⁹⁸(99-digit number)

21056269456891881205…91566318480609689600

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

2.105 × 10⁹⁸(99-digit number)

21056269456891881205…91566318480609689601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.211 × 10⁹⁸(99-digit number)

42112538913783762410…83132636961219379201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.422 × 10⁹⁸(99-digit number)

84225077827567524820…66265273922438758401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.684 × 10⁹⁹(100-digit number)

16845015565513504964…32530547844877516801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.369 × 10⁹⁹(100-digit number)

33690031131027009928…65061095689755033601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.738 × 10⁹⁹(100-digit number)

67380062262054019856…30122191379510067201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.347 × 10¹⁰⁰(101-digit number)

13476012452410803971…60244382759020134401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.695 × 10¹⁰⁰(101-digit number)

26952024904821607942…20488765518040268801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.390 × 10¹⁰⁰(101-digit number)

53904049809643215885…40977531036080537601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.078 × 10¹⁰¹(102-digit number)

10780809961928643177…81955062072161075201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.156 × 10¹⁰¹(102-digit number)

21561619923857286354…63910124144322150401

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2845289

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 b7fe08a4bbd774748a16add83647ae8809fdc9118c6385c13b42e6819393d01d

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 #2,845,289 on Chainz ↗

Block #2,845,289

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