Block #350,566

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/9/2014, 3:44:00 AM · Difficulty 10.2854 · 6,476,007 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9a32019b551afde774792dafac0d920674fc6f4db2b36bbefe6b0ad7ac51c786

View on Chainz ↗

Height

#350,566

Difficulty

10.285446

Transactions

Size

208 B

Version

Bits

0a4912f7

Nonce

524,670

Timestamp

1/9/2014, 3:44:00 AM

Confirmations

6,476,007

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

946075d74db6c768c6d00fe9f9d6ec9eae36b55a766723299369466a2a0f5871

Transactions (1)

Coinbase946075d74db6c7…69466a2a0f5871

1 in → 1 out9.4400 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.

1.433 × 10⁹⁹(100-digit number)

14337251416375522190…98074585527393654081

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

1.433 × 10⁹⁹(100-digit number)

14337251416375522190…98074585527393654081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.867 × 10⁹⁹(100-digit number)

28674502832751044381…96149171054787308161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.734 × 10⁹⁹(100-digit number)

57349005665502088763…92298342109574616321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.146 × 10¹⁰⁰(101-digit number)

11469801133100417752…84596684219149232641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.293 × 10¹⁰⁰(101-digit number)

22939602266200835505…69193368438298465281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.587 × 10¹⁰⁰(101-digit number)

45879204532401671010…38386736876596930561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.175 × 10¹⁰⁰(101-digit number)

91758409064803342021…76773473753193861121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.835 × 10¹⁰¹(102-digit number)

18351681812960668404…53546947506387722241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.670 × 10¹⁰¹(102-digit number)

36703363625921336808…07093895012775444481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.340 × 10¹⁰¹(102-digit number)

73406727251842673617…14187790025550888961

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #350,566

Cookie Preferences