Block #267,720

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/21/2013, 12:35:07 PM · Difficulty 9.9586 · 6,523,286 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

64f51ad4a6604678741f7e465b37ad08dca5c7e34cedfd93c0bb89956103c5b7

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Height

#267,720

Difficulty

9.958570

Transactions

Size

1.24 KB

Version

Bits

09f564d5

Nonce

2,276

Timestamp

11/21/2013, 12:35:07 PM

Confirmations

6,523,286

Merkle Root

7895d7cd2192cefbaf348cef16e30c2603769562d130ab83705397350adcd0a7

Transactions (2)

Coinbaseaf2f9ee0f3113f…4ec344b95ff07e

1 in → 2 out10.0900 XPM141 B

AdGRRh1e…QmctLb24 AHsw4d6U…EnM8UXNZ

f7ec829f7313d4…ef26a75e14e1d5

6 in → 5 out12.4867 XPM1.01 KB

AbrxnfNC…nEpWGHhc AGL4LiqG…EV8dqG2J AMuPGPXT…eMMNvd8v AeKNrjNj…1NEq95Ta AUfa5LFJ…C4BhhWGa

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.

1.196 × 10¹⁰¹(102-digit number)

11967318712845004737…77717275354865391501

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

1.196 × 10¹⁰¹(102-digit number)

11967318712845004737…77717275354865391501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.393 × 10¹⁰¹(102-digit number)

23934637425690009474…55434550709730783001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.786 × 10¹⁰¹(102-digit number)

47869274851380018948…10869101419461566001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.573 × 10¹⁰¹(102-digit number)

95738549702760037897…21738202838923132001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.914 × 10¹⁰²(103-digit number)

19147709940552007579…43476405677846264001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.829 × 10¹⁰²(103-digit number)

38295419881104015159…86952811355692528001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.659 × 10¹⁰²(103-digit number)

76590839762208030318…73905622711385056001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.531 × 10¹⁰³(104-digit number)

15318167952441606063…47811245422770112001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.063 × 10¹⁰³(104-digit number)

30636335904883212127…95622490845540224001

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer