Block #396,534

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/9/2014, 11:33:51 AM · Difficulty 10.4127 · 6,396,531 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

be4e09b371eb0106eacdb457b85b179cf7770a87282da78334c5ad5267ea228b

View on Chainz ↗

Height

#396,534

Difficulty

10.412721

Transactions

Size

1.13 KB

Version

Bits

0a69a817

Nonce

183,498

Timestamp

2/9/2014, 11:33:51 AM

Confirmations

6,396,531

Merkle Root

62adabb07af29cad0a4cd3ea27e3858f4c0b7711ccf4d7c9625ee6f797e4f755

Transactions (2)

Coinbase5ac6a75f9b9f03…ca351407b2f71f

1 in → 23 out9.2100 XPM845 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AYRvXuTr…CkbwFeLY

1ccd1cad98a4d3…93e0c51f9d1369

1 in → 2 out3.0126 XPM226 B

AY9afAnQ…kmcZZJR1 ARyQiN4d…yW1qNXWF

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.

2.674 × 10⁹³(94-digit number)

26748147158402778226…70923809044235392149

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

2.674 × 10⁹³(94-digit number)

26748147158402778226…70923809044235392149

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.349 × 10⁹³(94-digit number)

53496294316805556453…41847618088470784299

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.069 × 10⁹⁴(95-digit number)

10699258863361111290…83695236176941568599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.139 × 10⁹⁴(95-digit number)

21398517726722222581…67390472353883137199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.279 × 10⁹⁴(95-digit number)

42797035453444445162…34780944707766274399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.559 × 10⁹⁴(95-digit number)

85594070906888890325…69561889415532548799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.711 × 10⁹⁵(96-digit number)

17118814181377778065…39123778831065097599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.423 × 10⁹⁵(96-digit number)

34237628362755556130…78247557662130195199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.847 × 10⁹⁵(96-digit number)

68475256725511112260…56495115324260390399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.369 × 10⁹⁶(97-digit number)

13695051345102222452…12990230648520780799

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