Block #232,455

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/29/2013, 3:12:33 AM · Difficulty 9.9411 · 6,562,949 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2f46ce91aa1e2b9ed9bdd593411d6e59749c7cfe6b39a2f5c44f7a3751cc38af

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Height

#232,455

Difficulty

9.941075

Transactions

Size

1.64 KB

Version

Bits

09f0ea48

Nonce

127,742

Timestamp

10/29/2013, 3:12:33 AM

Confirmations

6,562,949

Mined by

⛏️ Ro'fAeNjg8HA2JzrdQD3LcJMTkwYEE9AkdpcSC

Merkle Root

f2364e177b8bc6e65d3e0e65e0894fa72938df507c7040dbda38a844c40c1a68

Transactions (1)

Coinbasef2364e177b8bc6…38a844c40c1a68

1 in → 45 out10.0800 XPM1.55 KB

AeNjg8HA…9AkdpcSC AeBk6YnL…JRXHDtz8 AeEcSGAf…HjtsPDKX APVGazMT…cDCk2nwA ANuKx9Ke…wm7nrBRq

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.

1.309 × 10⁸⁹(90-digit number)

13097701807474536424…15122412952447144961

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

1.309 × 10⁸⁹(90-digit number)

13097701807474536424…15122412952447144961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.619 × 10⁸⁹(90-digit number)

26195403614949072849…30244825904894289921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.239 × 10⁸⁹(90-digit number)

52390807229898145698…60489651809788579841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.047 × 10⁹⁰(91-digit number)

10478161445979629139…20979303619577159681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.095 × 10⁹⁰(91-digit number)

20956322891959258279…41958607239154319361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.191 × 10⁹⁰(91-digit number)

41912645783918516558…83917214478308638721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.382 × 10⁹⁰(91-digit number)

83825291567837033117…67834428956617277441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.676 × 10⁹¹(92-digit number)

16765058313567406623…35668857913234554881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.353 × 10⁹¹(92-digit number)

33530116627134813247…71337715826469109761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.706 × 10⁹¹(92-digit number)

67060233254269626494…42675431652938219521

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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, …

Cross-reference on Chainz Explorer