Block #321,326

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/20/2013, 6:04:25 AM · Difficulty 10.1897 · 6,474,651 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

745e7dc8ea9959ff453496bf754d819e727aa0ca9602a0dc6b969e07d4bc87f9

View on Chainz ↗

Height

#321,326

Difficulty

10.189664

Transactions

Size

1.05 KB

Version

Bits

0a308dda

Nonce

26,261

Timestamp

12/20/2013, 6:04:25 AM

Confirmations

6,474,651

Mined by

⛏️ .aR>Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

470d5959ac5135ea96bb8badd0e9ee0970423f4dbe09ad8fe241fa796f8f603b

Transactions (1)

Coinbase470d5959ac5135…41fa796f8f603b

1 in → 27 out9.6200 XPM981 B

Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AG5YAjec…VhA4Aeh1 AZemWJAo…6jhDtieG AZ2pPuKg…95SN2Yr7

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.

4.451 × 10⁹⁸(99-digit number)

44518956475368746409…84360319452866511361

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

4.451 × 10⁹⁸(99-digit number)

44518956475368746409…84360319452866511361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.903 × 10⁹⁸(99-digit number)

89037912950737492819…68720638905733022721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.780 × 10⁹⁹(100-digit number)

17807582590147498563…37441277811466045441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.561 × 10⁹⁹(100-digit number)

35615165180294997127…74882555622932090881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.123 × 10⁹⁹(100-digit number)

71230330360589994255…49765111245864181761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.424 × 10¹⁰⁰(101-digit number)

14246066072117998851…99530222491728363521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.849 × 10¹⁰⁰(101-digit number)

28492132144235997702…99060444983456727041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.698 × 10¹⁰⁰(101-digit number)

56984264288471995404…98120889966913454081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.139 × 10¹⁰¹(102-digit number)

11396852857694399080…96241779933826908161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.279 × 10¹⁰¹(102-digit number)

22793705715388798161…92483559867653816321

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