Block #496,796

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/17/2014, 6:48:55 AM · Difficulty 10.7588 · 6,295,195 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0b03260f8f57a5ab7fb5062a954058fd1ca9dc0d40cc1391e15d20ab9f9e1cb0

View on Chainz ↗

Height

#496,796

Difficulty

10.758783

Transactions

Size

866 B

Version

Bits

0ac23f98

Nonce

288,017

Timestamp

4/17/2014, 6:48:55 AM

Confirmations

6,295,195

Merkle Root

9070b2d8a065e92df9ff2925986751e7d986de9dbf7cd3106db568b6c3179d56

Transactions (1)

Coinbase9070b2d8a065e9…b568b6c3179d56

1 in → 21 out8.6300 XPM777 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AWMrD5hP…ZwsoxvZ3 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.

6.538 × 10⁹¹(92-digit number)

65388647103151984571…10590424241764078079

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

6.538 × 10⁹¹(92-digit number)

65388647103151984571…10590424241764078079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.307 × 10⁹²(93-digit number)

13077729420630396914…21180848483528156159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.615 × 10⁹²(93-digit number)

26155458841260793828…42361696967056312319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.231 × 10⁹²(93-digit number)

52310917682521587657…84723393934112624639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.046 × 10⁹³(94-digit number)

10462183536504317531…69446787868225249279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.092 × 10⁹³(94-digit number)

20924367073008635062…38893575736450498559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.184 × 10⁹³(94-digit number)

41848734146017270125…77787151472900997119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.369 × 10⁹³(94-digit number)

83697468292034540251…55574302945801994239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.673 × 10⁹⁴(95-digit number)

16739493658406908050…11148605891603988479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.347 × 10⁹⁴(95-digit number)

33478987316813816100…22297211783207976959

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer