Block #396,935

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/9/2014, 5:49:14 PM · Difficulty 10.4159 · 6,408,835 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

feecf344d04effabbd96b99a526b2080e55841efbc3f69b3daade962777569cc

View on Chainz ↗

Height

#396,935

Difficulty

10.415898

Transactions

Size

968 B

Version

Bits

0a6a7849

Nonce

33,812

Timestamp

2/9/2014, 5:49:14 PM

Confirmations

6,408,835

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

258a7273e41dc57178334a833affe6c303d2baa80c01a3f220d7f4c5078c9285

Transactions (1)

Coinbase258a7273e41dc5…d7f4c5078c9285

1 in → 24 out9.2000 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

3.443 × 10⁹¹(92-digit number)

34430704395958244751…96856575995594221581

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

3.443 × 10⁹¹(92-digit number)

34430704395958244751…96856575995594221581

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.886 × 10⁹¹(92-digit number)

68861408791916489502…93713151991188443161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.377 × 10⁹²(93-digit number)

13772281758383297900…87426303982376886321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.754 × 10⁹²(93-digit number)

27544563516766595801…74852607964753772641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.508 × 10⁹²(93-digit number)

55089127033533191602…49705215929507545281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.101 × 10⁹³(94-digit number)

11017825406706638320…99410431859015090561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.203 × 10⁹³(94-digit number)

22035650813413276640…98820863718030181121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.407 × 10⁹³(94-digit number)

44071301626826553281…97641727436060362241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.814 × 10⁹³(94-digit number)

88142603253653106563…95283454872120724481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.762 × 10⁹⁴(95-digit number)

17628520650730621312…90566909744241448961

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