Block #264,406

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/18/2013, 3:58:07 PM · Difficulty 9.9646 · 6,530,108 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a772e7581e36c339f6595f8b8a4d4c4396f6dbe5887915575315a9a428ec1df2

View on Chainz ↗

Height

#264,406

Difficulty

9.964560

Transactions

Size

1.38 KB

Version

Bits

09f6ed61

Nonce

4,765

Timestamp

11/18/2013, 3:58:07 PM

Confirmations

6,530,108

Mined by

⛏️ aR8AXRun4JxzeEWfpnmGdz6b2xb8yReRaSdaU

Merkle Root

1cab86d3a1d689c76794cf9c6acd001b260a2866f9570692278de13889ce4ae2

Transactions (1)

Coinbase1cab86d3a1d689…8de13889ce4ae2

1 in → 37 out10.0396 XPM1.29 KB

AXRun4Jx…ReRaSdaU ANHbaxZp…XjnHCJJs AaXrHDKv…J6ZMrwYz AGBnsf1M…FxQVAj3Q Aaf3yuJg…fCrhFXXe

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.

9.207 × 10¹⁰¹(102-digit number)

92072879344910476528…94616882534506495999

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

9.207 × 10¹⁰¹(102-digit number)

92072879344910476528…94616882534506495999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.841 × 10¹⁰²(103-digit number)

18414575868982095305…89233765069012991999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.682 × 10¹⁰²(103-digit number)

36829151737964190611…78467530138025983999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.365 × 10¹⁰²(103-digit number)

73658303475928381222…56935060276051967999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.473 × 10¹⁰³(104-digit number)

14731660695185676244…13870120552103935999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.946 × 10¹⁰³(104-digit number)

29463321390371352489…27740241104207871999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.892 × 10¹⁰³(104-digit number)

58926642780742704978…55480482208415743999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.178 × 10¹⁰⁴(105-digit number)

11785328556148540995…10960964416831487999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.357 × 10¹⁰⁴(105-digit number)

23570657112297081991…21921928833662975999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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