Block #515,007

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/28/2014, 12:46:58 PM · Difficulty 10.8397 · 6,280,472 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7122b3b1d25c74ecfd48a7d2ba2b0e821ffe16eea508bffc3e94b6b1450d569d

View on Chainz ↗

Height

#515,007

Difficulty

10.839664

Transactions

Size

717 B

Version

Bits

0ad6f43d

Nonce

36,840,549

Timestamp

4/28/2014, 12:46:58 PM

Confirmations

6,280,472

Mined by

⛏️ P2SHANrrHxu8kFr5M4GC5Cqzj9PEXSk2Fq4fqC

Merkle Root

ca27b2724500df3318144d2101ab73beab771cf40cb8cb224f451a6076f34b00

Transactions (2)

Coinbase9310a3ef109b77…f65e2f5489d00d

1 in → 1 out8.5100 XPM109 B

ANrrHxu8…k2Fq4fqC

0c05790336d1af…3c3239e101a860

3 in → 2 out0.5317 XPM520 B

AGdWVjRk…LFVsqCnK ASctJ1U2…6sHmQSKh

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.

6.552 × 10⁸⁹(90-digit number)

65527537971959629292…82854834212175899839

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

6.552 × 10⁸⁹(90-digit number)

65527537971959629292…82854834212175899839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.310 × 10⁹⁰(91-digit number)

13105507594391925858…65709668424351799679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.621 × 10⁹⁰(91-digit number)

26211015188783851717…31419336848703599359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.242 × 10⁹⁰(91-digit number)

52422030377567703434…62838673697407198719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.048 × 10⁹¹(92-digit number)

10484406075513540686…25677347394814397439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.096 × 10⁹¹(92-digit number)

20968812151027081373…51354694789628794879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.193 × 10⁹¹(92-digit number)

41937624302054162747…02709389579257589759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.387 × 10⁹¹(92-digit number)

83875248604108325494…05418779158515179519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.677 × 10⁹²(93-digit number)

16775049720821665098…10837558317030359039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.355 × 10⁹²(93-digit number)

33550099441643330197…21675116634060718079

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer