Block #264,954

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/19/2013, 3:35:11 AM · Difficulty 9.9635 · 6,538,828 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6e9eb601d8454d29083bf92a9786cc197b7a3b5159cd081bf235844efe2b90db

View on Chainz ↗

Height

#264,954

Difficulty

9.963510

Transactions

Size

2.01 KB

Version

Bits

09f6a88f

Nonce

283,382

Timestamp

11/19/2013, 3:35:11 AM

Confirmations

6,538,828

Mined by

⛏️ aREARskhKebzwhUsQms8dTj78qtmaUgDvvX9P

Merkle Root

430ca0630508f6d9914c83ec819c517f84e21d03a8cc400cef356373326f4b9d

Transactions (1)

Coinbase430ca0630508f6…356373326f4b9d

1 in → 56 out10.0400 XPM1.92 KB

ARskhKeb…UgDvvX9P ATTqakAA…DXMPsyzZ APZy8y6E…QZaGQjfp ANsrD1P6…m3RxY4uj AWjDtGT9…njnfkBxG

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.

1.238 × 10⁹⁸(99-digit number)

12381185058297830344…59605424133920602239

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

1.238 × 10⁹⁸(99-digit number)

12381185058297830344…59605424133920602239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.476 × 10⁹⁸(99-digit number)

24762370116595660688…19210848267841204479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.952 × 10⁹⁸(99-digit number)

49524740233191321376…38421696535682408959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.904 × 10⁹⁸(99-digit number)

99049480466382642753…76843393071364817919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.980 × 10⁹⁹(100-digit number)

19809896093276528550…53686786142729635839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.961 × 10⁹⁹(100-digit number)

39619792186553057101…07373572285459271679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.923 × 10⁹⁹(100-digit number)

79239584373106114202…14747144570918543359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.584 × 10¹⁰⁰(101-digit number)

15847916874621222840…29494289141837086719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.169 × 10¹⁰⁰(101-digit number)

31695833749242445681…58988578283674173439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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