Block #328,636

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/25/2013, 10:31:36 AM · Difficulty 10.1658 · 6,465,774 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3b23f5a51f9b578a1c6bb668b1ce25c6e81774dbcc1722f7a8209863b757eb05

View on Chainz ↗

Height

#328,636

Difficulty

10.165758

Transactions

Size

1.05 KB

Version

Bits

0a2a6f16

Nonce

12,025

Timestamp

12/25/2013, 10:31:36 AM

Confirmations

6,465,774

Mined by

⛏️ aRYAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

c6ff6b16c3f981e4c8c85ca9d9cac52d2e4154b5c71185521a06b1a99ff84d7c

Transactions (1)

Coinbasec6ff6b16c3f981…06b1a99ff84d7c

1 in → 27 out9.6344 XPM981 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AG5YAjec…VhA4Aeh1 AFutDVqJ…TJTJj6UF

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.

5.693 × 10⁹³(94-digit number)

56937060419354542507…64243850585439655681

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

5.693 × 10⁹³(94-digit number)

56937060419354542507…64243850585439655681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.138 × 10⁹⁴(95-digit number)

11387412083870908501…28487701170879311361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.277 × 10⁹⁴(95-digit number)

22774824167741817002…56975402341758622721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.554 × 10⁹⁴(95-digit number)

45549648335483634005…13950804683517245441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.109 × 10⁹⁴(95-digit number)

91099296670967268011…27901609367034490881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.821 × 10⁹⁵(96-digit number)

18219859334193453602…55803218734068981761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.643 × 10⁹⁵(96-digit number)

36439718668386907204…11606437468137963521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.287 × 10⁹⁵(96-digit number)

72879437336773814409…23212874936275927041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.457 × 10⁹⁶(97-digit number)

14575887467354762881…46425749872551854081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.915 × 10⁹⁶(97-digit number)

29151774934709525763…92851499745103708161

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