Block #478,784

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/7/2014, 7:23:26 AM · Difficulty 10.4969 · 6,329,523 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

20653c0f157e55b5889ee1c00d74ac091286f8f8e943c4aa5fc9a210d784f67a

View on Chainz ↗

Height

#478,784

Difficulty

10.496874

Transactions

Size

898 B

Version

Bits

0a7f332a

Nonce

109,302

Timestamp

4/7/2014, 7:23:26 AM

Confirmations

6,329,523

Mined by

⛏️ @NAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

e446ee122ce7066376873c87f9e7a7465c89a3de2bedd768c6c904659a6b03ff

Transactions (1)

Coinbasee446ee122ce706…c904659a6b03ff

1 in → 22 out9.0600 XPM811 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh ATp4jJhs…TbSgR8Qb AUFKXvnz…342ApNcm AMW1p9oT…2TzdaZxH

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.

8.359 × 10⁸⁷(88-digit number)

83591330421259145023…59649665660659546821

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

8.359 × 10⁸⁷(88-digit number)

83591330421259145023…59649665660659546821

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.671 × 10⁸⁸(89-digit number)

16718266084251829004…19299331321319093641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.343 × 10⁸⁸(89-digit number)

33436532168503658009…38598662642638187281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.687 × 10⁸⁸(89-digit number)

66873064337007316018…77197325285276374561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.337 × 10⁸⁹(90-digit number)

13374612867401463203…54394650570552749121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.674 × 10⁸⁹(90-digit number)

26749225734802926407…08789301141105498241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.349 × 10⁸⁹(90-digit number)

53498451469605852815…17578602282210996481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.069 × 10⁹⁰(91-digit number)

10699690293921170563…35157204564421992961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.139 × 10⁹⁰(91-digit number)

21399380587842341126…70314409128843985921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.279 × 10⁹⁰(91-digit number)

42798761175684682252…40628818257687971841

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

Block #478,784

Cookie Preferences