Block #348,287

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/7/2014, 5:14:10 PM · Difficulty 10.2545 · 6,459,553 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

204fe1255221c48dd61b2746b869e7448c6afe2875a996ddfc784a0af536d210

View on Chainz ↗

Height

#348,287

Difficulty

10.254461

Transactions

Size

213 B

Version

Bits

0a41245b

Nonce

21,295

Timestamp

1/7/2014, 5:14:10 PM

Confirmations

6,459,553

Mined by

⛏️ P2SHAd6bt69SstZerhCFqTfZCFaUaRPfMPqrnD

Merkle Root

6fcc96503d43a0f31e996f0d9c433be117d5ef77e2057aef6855b5096f35b4fc

Transactions (1)

Coinbase6fcc96503d43a0…55b5096f35b4fc

1 in → 1 out9.5000 XPM118 B

Ad6bt69S…PfMPqrnD

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.

2.446 × 10¹⁰⁶(107-digit number)

24464365662420480158…47644471587519856641

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

2.446 × 10¹⁰⁶(107-digit number)

24464365662420480158…47644471587519856641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.892 × 10¹⁰⁶(107-digit number)

48928731324840960316…95288943175039713281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.785 × 10¹⁰⁶(107-digit number)

97857462649681920632…90577886350079426561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.957 × 10¹⁰⁷(108-digit number)

19571492529936384126…81155772700158853121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.914 × 10¹⁰⁷(108-digit number)

39142985059872768252…62311545400317706241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.828 × 10¹⁰⁷(108-digit number)

78285970119745536505…24623090800635412481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.565 × 10¹⁰⁸(109-digit number)

15657194023949107301…49246181601270824961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.131 × 10¹⁰⁸(109-digit number)

31314388047898214602…98492363202541649921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.262 × 10¹⁰⁸(109-digit number)

62628776095796429204…96984726405083299841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.252 × 10¹⁰⁹(110-digit number)

12525755219159285840…93969452810166599681

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 #348,287

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