Block #374,291

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2014, 10:12:18 PM · Difficulty 10.4240 · 6,438,286 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

1f333efd7629669ec5cef5c4ec5e1a5ddae6aace6455279cc29ca000d8fa970b

View on Chainz ↗

Height

#374,291

Difficulty

10.424017

Transactions

Size

208 B

Version

Bits

0a6c8c5f

Nonce

16,800

Timestamp

1/24/2014, 10:12:18 PM

Confirmations

6,438,286

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

43751fe63402e01c8778ae152a39871701bb67c1399033f6aa113956c5409b84

Transactions (1)

Coinbase43751fe63402e0…113956c5409b84

1 in → 1 out9.1900 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.

2.427 × 10⁹⁸(99-digit number)

24274166535816995163…33135941899120131201

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

2.427 × 10⁹⁸(99-digit number)

24274166535816995163…33135941899120131201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.854 × 10⁹⁸(99-digit number)

48548333071633990327…66271883798240262401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.709 × 10⁹⁸(99-digit number)

97096666143267980655…32543767596480524801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.941 × 10⁹⁹(100-digit number)

19419333228653596131…65087535192961049601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.883 × 10⁹⁹(100-digit number)

38838666457307192262…30175070385922099201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.767 × 10⁹⁹(100-digit number)

77677332914614384524…60350140771844198401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.553 × 10¹⁰⁰(101-digit number)

15535466582922876904…20700281543688396801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.107 × 10¹⁰⁰(101-digit number)

31070933165845753809…41400563087376793601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.214 × 10¹⁰⁰(101-digit number)

62141866331691507619…82801126174753587201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.242 × 10¹⁰¹(102-digit number)

12428373266338301523…65602252349507174401

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 #374,291

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