Block #347,005

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/6/2014, 9:44:03 PM · Difficulty 10.2377 · 6,464,007 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e115c05352d036f071062d7c21974ce643aa080d14fdbf4b32f752f925f29c51

View on Chainz ↗

Height

#347,005

Difficulty

10.237684

Transactions

Size

209 B

Version

Bits

0a3cd8d4

Nonce

977

Timestamp

1/6/2014, 9:44:03 PM

Confirmations

6,464,007

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7652fb09f3c1233b79ada912ca8f52232763c51d1f14c84a4aaecc20bafe8821

Transactions (1)

Coinbase7652fb09f3c123…aecc20bafe8821

1 in → 1 out9.5300 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.

7.665 × 10¹⁰¹(102-digit number)

76656066674983858026…70215526864492953599

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

7.665 × 10¹⁰¹(102-digit number)

76656066674983858026…70215526864492953599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.533 × 10¹⁰²(103-digit number)

15331213334996771605…40431053728985907199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.066 × 10¹⁰²(103-digit number)

30662426669993543210…80862107457971814399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.132 × 10¹⁰²(103-digit number)

61324853339987086420…61724214915943628799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.226 × 10¹⁰³(104-digit number)

12264970667997417284…23448429831887257599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.452 × 10¹⁰³(104-digit number)

24529941335994834568…46896859663774515199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.905 × 10¹⁰³(104-digit number)

49059882671989669136…93793719327549030399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.811 × 10¹⁰³(104-digit number)

98119765343979338273…87587438655098060799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.962 × 10¹⁰⁴(105-digit number)

19623953068795867654…75174877310196121599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.924 × 10¹⁰⁴(105-digit number)

39247906137591735309…50349754620392243199

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 #347,005

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