Block #276,532

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/27/2013, 5:34:00 AM · Difficulty 9.9634 · 6,531,654 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

dba732d3d578e68d53d3c945e17b0ebee7cd65f5cc2a4a60c803616085a8f112

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Height

#276,532

Difficulty

9.963435

Transactions

Size

1.14 KB

Version

Bits

09f6a3a5

Nonce

41,669

Timestamp

11/27/2013, 5:34:00 AM

Confirmations

6,531,654

Mined by

⛏️ 48aRAe7UyoY4jm5kmJspmVRNUvXqMHDtgAv9cY

Merkle Root

b263d47f7cf3157df308c3d59f3ea36567e45e20e029e3cdec96689e19782753

Transactions (1)

Coinbaseb263d47f7cf315…96689e19782753

1 in → 30 out10.0400 XPM1.06 KB

Ae7UyoY4…DtgAv9cY Ab3J4ipo…GaHrWuuW AXzcEfhQ…Dz9wL2mD AaSot6r4…DjoWHEUX AaZptiTm…mxymWwAJ

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.

4.333 × 10⁹²(93-digit number)

43332041247983430125…09201934462111805441

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

4.333 × 10⁹²(93-digit number)

43332041247983430125…09201934462111805441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.666 × 10⁹²(93-digit number)

86664082495966860251…18403868924223610881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.733 × 10⁹³(94-digit number)

17332816499193372050…36807737848447221761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.466 × 10⁹³(94-digit number)

34665632998386744100…73615475696894443521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.933 × 10⁹³(94-digit number)

69331265996773488201…47230951393788887041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.386 × 10⁹⁴(95-digit number)

13866253199354697640…94461902787577774081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.773 × 10⁹⁴(95-digit number)

27732506398709395280…88923805575155548161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.546 × 10⁹⁴(95-digit number)

55465012797418790560…77847611150311096321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.109 × 10⁹⁵(96-digit number)

11093002559483758112…55695222300622192641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.218 × 10⁹⁵(96-digit number)

22186005118967516224…11390444601244385281

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 #276,532

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