Block #522,438

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/3/2014, 1:05:49 AM · Difficulty 10.8671 · 6,285,959 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

12aa3e4de7e5bc1e3734447544e22bf56e623b23fd65e60c67af7fdb6a0abc86

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Height

#522,438

Difficulty

10.867101

Transactions

Size

208 B

Version

Bits

0addfa51

Nonce

16,952,836

Timestamp

5/3/2014, 1:05:49 AM

Confirmations

6,285,959

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7580375244fc332a4e2dea9ce18dff4466f8801a778d5eca0515d691761eaf0b

Transactions (1)

Coinbase7580375244fc33…15d691761eaf0b

1 in → 1 out8.4500 XPM116 B

AbwWkWZt…kawDhufa

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.

8.824 × 10⁹⁸(99-digit number)

88249573938032128566…09721003344187235241

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

8.824 × 10⁹⁸(99-digit number)

88249573938032128566…09721003344187235241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.764 × 10⁹⁹(100-digit number)

17649914787606425713…19442006688374470481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.529 × 10⁹⁹(100-digit number)

35299829575212851426…38884013376748940961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.059 × 10⁹⁹(100-digit number)

70599659150425702853…77768026753497881921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.411 × 10¹⁰⁰(101-digit number)

14119931830085140570…55536053506995763841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.823 × 10¹⁰⁰(101-digit number)

28239863660170281141…11072107013991527681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.647 × 10¹⁰⁰(101-digit number)

56479727320340562282…22144214027983055361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.129 × 10¹⁰¹(102-digit number)

11295945464068112456…44288428055966110721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.259 × 10¹⁰¹(102-digit number)

22591890928136224913…88576856111932221441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.518 × 10¹⁰¹(102-digit number)

45183781856272449826…77153712223864442881

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

Block #522,438

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