Block #54,304

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 7:45:46 PM · Difficulty 8.9321 · 6,749,099 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b3b926c793f04d542223556f74776a9fce6bfb07d06a62d11aa6d6ee6f9fe425

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Height

#54,304

Difficulty

8.932147

Transactions

Size

203 B

Version

Bits

08eea129

Nonce

411

Timestamp

7/16/2013, 7:45:46 PM

Confirmations

6,749,099

Mined by

⛏️ P2SHAJbRF9Vh3Pm1qDnFdVGkh4jvYocmDMZyVK

Merkle Root

572910fbc96fa4c40db8d12d6408fa533137ff9cccc765e6606b92b0aaa180f2

Transactions (1)

Coinbase572910fbc96fa4…6b92b0aaa180f2

1 in → 1 out12.5200 XPM110 B

AJbRF9Vh…cmDMZyVK

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.

4.549 × 10¹⁰¹(102-digit number)

45496591735453522776…71286870291474347061

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

4.549 × 10¹⁰¹(102-digit number)

45496591735453522776…71286870291474347061

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.099 × 10¹⁰¹(102-digit number)

90993183470907045552…42573740582948694121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.819 × 10¹⁰²(103-digit number)

18198636694181409110…85147481165897388241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.639 × 10¹⁰²(103-digit number)

36397273388362818220…70294962331794776481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.279 × 10¹⁰²(103-digit number)

72794546776725636441…40589924663589552961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.455 × 10¹⁰³(104-digit number)

14558909355345127288…81179849327179105921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.911 × 10¹⁰³(104-digit number)

29117818710690254576…62359698654358211841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.823 × 10¹⁰³(104-digit number)

58235637421380509153…24719397308716423681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.164 × 10¹⁰⁴(105-digit number)

11647127484276101830…49438794617432847361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.329 × 10¹⁰⁴(105-digit number)

23294254968552203661…98877589234865694721

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