Block #331,422

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/27/2013, 8:54:40 AM · Difficulty 10.1670 · 6,495,660 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5b26dc5858da502ed742d698d80fb17d03a8d4d1031c9bac82351cdff24379ee

View on Chainz ↗

Height

#331,422

Difficulty

10.167041

Transactions

Size

207 B

Version

Bits

0a2ac33b

Nonce

87,668

Timestamp

12/27/2013, 8:54:40 AM

Confirmations

6,495,660

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

932e0f658778b20d3d81c93cc9f6b498d212211e0b4ffe1f265c1fbed9da453c

Transactions (1)

Coinbase932e0f658778b2…5c1fbed9da453c

1 in → 1 out9.6600 XPM116 B

AbwWkWZt…kawDhufa

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.

1.091 × 10⁹⁸(99-digit number)

10916588242105101358…09539784541621405759

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

1.091 × 10⁹⁸(99-digit number)

10916588242105101358…09539784541621405759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.183 × 10⁹⁸(99-digit number)

21833176484210202716…19079569083242811519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.366 × 10⁹⁸(99-digit number)

43666352968420405432…38159138166485623039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.733 × 10⁹⁸(99-digit number)

87332705936840810864…76318276332971246079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.746 × 10⁹⁹(100-digit number)

17466541187368162172…52636552665942492159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.493 × 10⁹⁹(100-digit number)

34933082374736324345…05273105331884984319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.986 × 10⁹⁹(100-digit number)

69866164749472648691…10546210663769968639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.397 × 10¹⁰⁰(101-digit number)

13973232949894529738…21092421327539937279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.794 × 10¹⁰⁰(101-digit number)

27946465899789059476…42184842655079874559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.589 × 10¹⁰⁰(101-digit number)

55892931799578118953…84369685310159749119

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

Block #331,422

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