Block #327,452

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/24/2013, 1:33:36 PM · Difficulty 10.1780 · 6,467,947 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d860af5eaf1e31f86ac8ee36e45376f97982338923cfb7b4f37494f2a1f70d67

View on Chainz ↗

Height

#327,452

Difficulty

10.177975

Transactions

Size

1.04 KB

Version

Bits

0a2d8fbe

Nonce

431,425

Timestamp

12/24/2013, 1:33:36 PM

Confirmations

6,467,947

Mined by

⛏️ aRAMdvB6BSeR5j7BaEUYaiSNxidBDPq9FYdA

Merkle Root

cb228e8c70cd28b67bb534cdb850bc798be10b3b892c47b5fc06fa590edf723c

Transactions (1)

Coinbasecb228e8c70cd28…06fa590edf723c

1 in → 27 out9.6400 XPM981 B

AMdvB6BS…DPq9FYdA Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AeAvCqzy…VAJ6Bwj8 Ad9pSzHt…cpJ3y2zz

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.

3.879 × 10⁹¹(92-digit number)

38798079595672214571…00726173414508907521

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

3.879 × 10⁹¹(92-digit number)

38798079595672214571…00726173414508907521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.759 × 10⁹¹(92-digit number)

77596159191344429143…01452346829017815041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.551 × 10⁹²(93-digit number)

15519231838268885828…02904693658035630081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.103 × 10⁹²(93-digit number)

31038463676537771657…05809387316071260161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.207 × 10⁹²(93-digit number)

62076927353075543314…11618774632142520321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.241 × 10⁹³(94-digit number)

12415385470615108662…23237549264285040641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.483 × 10⁹³(94-digit number)

24830770941230217325…46475098528570081281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.966 × 10⁹³(94-digit number)

49661541882460434651…92950197057140162561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.932 × 10⁹³(94-digit number)

99323083764920869303…85900394114280325121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.986 × 10⁹⁴(95-digit number)

19864616752984173860…71800788228560650241

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