Block #331,605

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/27/2013, 11:49:21 AM · Difficulty 10.1683 · 6,471,779 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

31b09f5e7b61c46b520482f4ccb86098d20b6a14aa5d1eca7fa744a3beed02d2

View on Chainz ↗

Height

#331,605

Difficulty

10.168340

Transactions

Size

1.01 KB

Version

Bits

0a2b1855

Nonce

226,296

Timestamp

12/27/2013, 11:49:21 AM

Confirmations

6,471,779

Mined by

⛏️ UaRizAFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

f9af3d9b1c94d6c1ca7b116e93fed61d99b95d20924fe0c0efb2cbd8a1cfa83a

Transactions (1)

Coinbasef9af3d9b1c94d6…b2cbd8a1cfa83a

1 in → 26 out9.6600 XPM947 B

AFutDVqJ…TJTJj6UF AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 AMSvYdDV…AM3cN4zw

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.

4.522 × 10⁹⁴(95-digit number)

45222054988574691840…75380090295608782401

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

4.522 × 10⁹⁴(95-digit number)

45222054988574691840…75380090295608782401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.044 × 10⁹⁴(95-digit number)

90444109977149383681…50760180591217564801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.808 × 10⁹⁵(96-digit number)

18088821995429876736…01520361182435129601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.617 × 10⁹⁵(96-digit number)

36177643990859753472…03040722364870259201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.235 × 10⁹⁵(96-digit number)

72355287981719506945…06081444729740518401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.447 × 10⁹⁶(97-digit number)

14471057596343901389…12162889459481036801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.894 × 10⁹⁶(97-digit number)

28942115192687802778…24325778918962073601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.788 × 10⁹⁶(97-digit number)

57884230385375605556…48651557837924147201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.157 × 10⁹⁷(98-digit number)

11576846077075121111…97303115675848294401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.315 × 10⁹⁷(98-digit number)

23153692154150242222…94606231351696588801

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