Block #338,125

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/1/2014, 5:39:28 AM · Difficulty 10.1188 · 6,464,935 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

11adbb664efe00a985ad5ffe01c1c02db6116d28cc4003b34cf2f4af2aae02ab

View on Chainz ↗

Height

#338,125

Difficulty

10.118830

Transactions

Size

1.05 KB

Version

Bits

0a1e6ba8

Nonce

3,824

Timestamp

1/1/2014, 5:39:28 AM

Confirmations

6,464,935

Mined by

⛏️ aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

a4a143916ebac1b375b2eab8972466b95c4434836753356e4099d294c82550a1

Transactions (1)

Coinbasea4a143916ebac1…99d294c82550a1

1 in → 27 out9.7500 XPM981 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 AXeQnyEs…fUWKQwq8

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.

1.089 × 10⁹⁹(100-digit number)

10895074229686014073…51789601732767163999

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

1.089 × 10⁹⁹(100-digit number)

10895074229686014073…51789601732767163999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.179 × 10⁹⁹(100-digit number)

21790148459372028147…03579203465534327999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.358 × 10⁹⁹(100-digit number)

43580296918744056295…07158406931068655999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.716 × 10⁹⁹(100-digit number)

87160593837488112590…14316813862137311999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.743 × 10¹⁰⁰(101-digit number)

17432118767497622518…28633627724274623999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.486 × 10¹⁰⁰(101-digit number)

34864237534995245036…57267255448549247999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.972 × 10¹⁰⁰(101-digit number)

69728475069990490072…14534510897098495999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.394 × 10¹⁰¹(102-digit number)

13945695013998098014…29069021794196991999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.789 × 10¹⁰¹(102-digit number)

27891390027996196029…58138043588393983999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.578 × 10¹⁰¹(102-digit number)

55782780055992392058…16276087176787967999

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