Block #324,588

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/22/2013, 10:54:08 AM · Difficulty 10.2053 · 6,478,940 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4a9c14df085f7a3c97c82ffc5ba015cf085ff30073125da949bb9a75c6e49103

View on Chainz ↗

Height

#324,588

Difficulty

10.205338

Transactions

Size

1.01 KB

Version

Bits

0a349100

Nonce

212,961

Timestamp

12/22/2013, 10:54:08 AM

Confirmations

6,478,940

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

5ba1d978b8e77e0df4094c282729567f0473dc51816006bb7c23825929d6e709

Transactions (1)

Coinbase5ba1d978b8e77e…23825929d6e709

1 in → 26 out9.5900 XPM947 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AG5YAjec…VhA4Aeh1 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.

4.050 × 10⁹⁸(99-digit number)

40508214061365483406…92566610866750714841

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

4.050 × 10⁹⁸(99-digit number)

40508214061365483406…92566610866750714841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.101 × 10⁹⁸(99-digit number)

81016428122730966813…85133221733501429681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.620 × 10⁹⁹(100-digit number)

16203285624546193362…70266443467002859361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.240 × 10⁹⁹(100-digit number)

32406571249092386725…40532886934005718721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.481 × 10⁹⁹(100-digit number)

64813142498184773450…81065773868011437441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.296 × 10¹⁰⁰(101-digit number)

12962628499636954690…62131547736022874881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.592 × 10¹⁰⁰(101-digit number)

25925256999273909380…24263095472045749761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.185 × 10¹⁰⁰(101-digit number)

51850513998547818760…48526190944091499521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.037 × 10¹⁰¹(102-digit number)

10370102799709563752…97052381888182999041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.074 × 10¹⁰¹(102-digit number)

20740205599419127504…94104763776365998081

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