Block #491,266

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/14/2014, 9:56:04 AM · Difficulty 10.6805 · 6,312,190 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

579ab9dc78e0d486e72051f4efc4f8665371456694aafe20f9ea412ea6c7b78f

View on Chainz ↗

Height

#491,266

Difficulty

10.680473

Transactions

Size

763 B

Version

Bits

0aae3373

Nonce

75,237

Timestamp

4/14/2014, 9:56:04 AM

Confirmations

6,312,190

Mined by

⛏️ aSKAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

29bc481c6ad5f4a0d560bdf9a7881e97df1e6d86d718daf57f16849acbd4d9e5

Transactions (1)

Coinbase29bc481c6ad5f4…16849acbd4d9e5

1 in → 18 out8.7500 XPM675 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR AJtNW28X…Syb4Ph5j

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.

1.670 × 10⁹⁰(91-digit number)

16708397282941878366…26957310111020313181

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

1.670 × 10⁹⁰(91-digit number)

16708397282941878366…26957310111020313181

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.341 × 10⁹⁰(91-digit number)

33416794565883756732…53914620222040626361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.683 × 10⁹⁰(91-digit number)

66833589131767513465…07829240444081252721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.336 × 10⁹¹(92-digit number)

13366717826353502693…15658480888162505441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.673 × 10⁹¹(92-digit number)

26733435652707005386…31316961776325010881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.346 × 10⁹¹(92-digit number)

53466871305414010772…62633923552650021761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.069 × 10⁹²(93-digit number)

10693374261082802154…25267847105300043521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.138 × 10⁹²(93-digit number)

21386748522165604309…50535694210600087041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.277 × 10⁹²(93-digit number)

42773497044331208618…01071388421200174081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.554 × 10⁹²(93-digit number)

85546994088662417236…02142776842400348161

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