Block #264,796

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/19/2013, 12:18:26 AM · Difficulty 9.9638 · 6,560,516 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2ff03bc7c56c180edbcf42e3b3ca96501d63e51699be9626e6b92f333ed97d33

View on Chainz ↗

Height

#264,796

Difficulty

9.963766

Transactions

Size

1.58 KB

Version

Bits

09f6b961

Nonce

43,932

Timestamp

11/19/2013, 12:18:26 AM

Confirmations

6,560,516

Mined by

AYQ2FQaeZnbn2GCKnYcxePtL5b8g2PKK8n

Merkle Root

4d7b3dbc1d038ac4252584597bdbef5854c979d1b2517bdd6e752cb5d982f810

Transactions (1)

Coinbase4d7b3dbc1d038a…752cb5d982f810

1 in → 43 out10.0400 XPM1.49 KB

AYQ2FQae…8g2PKK8n APfZjrNu…Wvzt6AFp ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61 ATaiAP5C…o4tqgUvu

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.

5.307 × 10¹⁰⁰(101-digit number)

53070489660730505103…21238135088672742399

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

5.307 × 10¹⁰⁰(101-digit number)

53070489660730505103…21238135088672742399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.061 × 10¹⁰¹(102-digit number)

10614097932146101020…42476270177345484799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.122 × 10¹⁰¹(102-digit number)

21228195864292202041…84952540354690969599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.245 × 10¹⁰¹(102-digit number)

42456391728584404082…69905080709381939199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.491 × 10¹⁰¹(102-digit number)

84912783457168808165…39810161418763878399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.698 × 10¹⁰²(103-digit number)

16982556691433761633…79620322837527756799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.396 × 10¹⁰²(103-digit number)

33965113382867523266…59240645675055513599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.793 × 10¹⁰²(103-digit number)

67930226765735046532…18481291350111027199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.358 × 10¹⁰³(104-digit number)

13586045353147009306…36962582700222054399

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

Block #264,796

Cookie Preferences