Block #683,307

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/18/2014, 11:55:01 PM · Difficulty 10.9595 · 6,134,526 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

1eb0b519c8a1413341e35123f4070915daa8089edc0717eda61de1a0cb62ee31

View on Chainz ↗

Height

#683,307

Difficulty

10.959537

Transactions

Size

243 B

Version

Bits

0af5a43d

Nonce

682,990,901

Timestamp

8/18/2014, 11:55:01 PM

Confirmations

6,134,526

Mined by

⛏️ P2SHATrzKxLEMcqj8iissCT2aSSgyrdnfypiwk

Merkle Root

f152a2f6dc89c5e31931c3afcebe7346684224ca3a020e4a8f535a8823702865

Transactions (1)

Coinbasef152a2f6dc89c5…535a8823702865

1 in → 2 out8.3100 XPM152 B

ATrzKxLE…dnfypiwk ALPu3s2c…EJXLjVFh

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.

1.704 × 10⁹⁷(98-digit number)

17043341602395901125…48500496706824458241

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

1.704 × 10⁹⁷(98-digit number)

17043341602395901125…48500496706824458241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.408 × 10⁹⁷(98-digit number)

34086683204791802251…97000993413648916481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.817 × 10⁹⁷(98-digit number)

68173366409583604502…94001986827297832961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.363 × 10⁹⁸(99-digit number)

13634673281916720900…88003973654595665921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.726 × 10⁹⁸(99-digit number)

27269346563833441800…76007947309191331841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.453 × 10⁹⁸(99-digit number)

54538693127666883601…52015894618382663681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.090 × 10⁹⁹(100-digit number)

10907738625533376720…04031789236765327361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.181 × 10⁹⁹(100-digit number)

21815477251066753440…08063578473530654721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.363 × 10⁹⁹(100-digit number)

43630954502133506881…16127156947061309441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.726 × 10⁹⁹(100-digit number)

87261909004267013762…32254313894122618881

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 #683,307

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