Block #476,617

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/5/2014, 10:45:55 PM · Difficulty 10.4750 · 6,332,979 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

945887d126d7c0f3d476e88058d252387b4f5841e8b7eba2296cfb3538d03606

View on Chainz ↗

Height

#476,617

Difficulty

10.474995

Transactions

Size

932 B

Version

Bits

0a79994d

Nonce

77,318

Timestamp

4/5/2014, 10:45:55 PM

Confirmations

6,332,979

Mined by

⛏️ EpAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

8a60c277b7f1fb0f227f30d4ecd0c04322aadc6616072eadfc56503508ba577d

Transactions (1)

Coinbase8a60c277b7f1fb…56503508ba577d

1 in → 23 out9.1000 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ATp4jJhs…TbSgR8Qb AUFKXvnz…342ApNcm AWFABhGb…QWK99PRN

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.

3.121 × 10⁸⁸(89-digit number)

31218460746944977589…52245357577348151701

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

3.121 × 10⁸⁸(89-digit number)

31218460746944977589…52245357577348151701

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.243 × 10⁸⁸(89-digit number)

62436921493889955179…04490715154696303401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.248 × 10⁸⁹(90-digit number)

12487384298777991035…08981430309392606801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.497 × 10⁸⁹(90-digit number)

24974768597555982071…17962860618785213601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.994 × 10⁸⁹(90-digit number)

49949537195111964143…35925721237570427201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.989 × 10⁸⁹(90-digit number)

99899074390223928287…71851442475140854401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.997 × 10⁹⁰(91-digit number)

19979814878044785657…43702884950281708801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.995 × 10⁹⁰(91-digit number)

39959629756089571314…87405769900563417601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.991 × 10⁹⁰(91-digit number)

79919259512179142629…74811539801126835201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.598 × 10⁹¹(92-digit number)

15983851902435828525…49623079602253670401

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 #476,617

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