Block #267,731

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/21/2013, 12:53:05 PM · Difficulty 9.9585 · 6,534,857 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4ea85bafc5816c85d1254e2517c40f4303bbb00c3b8dbc2afff8a70585f4b0bf

View on Chainz ↗

Height

#267,731

Difficulty

9.958526

Transactions

Size

1.87 KB

Version

Bits

09f561f1

Nonce

178,447

Timestamp

11/21/2013, 12:53:05 PM

Confirmations

6,534,857

Mined by

⛏️ aRANEJ2uT8T2Pi7Zn9LkcbWFnmeGYefcaoXo

Merkle Root

9084a208dbdbd9ce8edcbb90bb4bb4bac71c5dcb283f873eb38a5844c70ec59d

Transactions (1)

Coinbase9084a208dbdbd9…8a5844c70ec59d

1 in → 52 out10.0500 XPM1.79 KB

ANEJ2uT8…YefcaoXo AFqKfjez…qX9Ace3g AQapNBe8…Pxk4vkev ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61

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.

3.747 × 10⁸⁹(90-digit number)

37478723362395926345…22691569602971991479

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

3.747 × 10⁸⁹(90-digit number)

37478723362395926345…22691569602971991479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.495 × 10⁸⁹(90-digit number)

74957446724791852690…45383139205943982959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.499 × 10⁹⁰(91-digit number)

14991489344958370538…90766278411887965919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.998 × 10⁹⁰(91-digit number)

29982978689916741076…81532556823775931839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.996 × 10⁹⁰(91-digit number)

59965957379833482152…63065113647551863679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.199 × 10⁹¹(92-digit number)

11993191475966696430…26130227295103727359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.398 × 10⁹¹(92-digit number)

23986382951933392860…52260454590207454719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.797 × 10⁹¹(92-digit number)

47972765903866785721…04520909180414909439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.594 × 10⁹¹(92-digit number)

95945531807733571443…09041818360829818879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.918 × 10⁹²(93-digit number)

19189106361546714288…18083636721659637759

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