Block #513,420

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/27/2014, 12:35:53 PM · Difficulty 10.8351 · 6,327,413 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f698d8b4aee76d176432d8f77351f9b05ecbd301547499339ef5f2f7a611d933

View on Chainz ↗

Height

#513,420

Difficulty

10.835137

Transactions

Size

202 B

Version

Bits

0ad5cb87

Nonce

16,710

Timestamp

4/27/2014, 12:35:53 PM

Confirmations

6,327,413

Mined by

⛏️ P2SHALTTwhmQLcGJchr7xhh4p3RNXUkVCkznsS

Merkle Root

a675a2240e578beeccb6217e01702aaa9d091ef3119920fef2565060e764c3b2

Transactions (1)

Coinbasea675a2240e578b…565060e764c3b2

1 in → 1 out8.5000 XPM111 B

ALTTwhmQ…kVCkznsS

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.

1.126 × 10⁹⁸(99-digit number)

11265695083079194627…35348707515873728321

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

1.126 × 10⁹⁸(99-digit number)

11265695083079194627…35348707515873728321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.253 × 10⁹⁸(99-digit number)

22531390166158389254…70697415031747456641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.506 × 10⁹⁸(99-digit number)

45062780332316778509…41394830063494913281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.012 × 10⁹⁸(99-digit number)

90125560664633557018…82789660126989826561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.802 × 10⁹⁹(100-digit number)

18025112132926711403…65579320253979653121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.605 × 10⁹⁹(100-digit number)

36050224265853422807…31158640507959306241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.210 × 10⁹⁹(100-digit number)

72100448531706845614…62317281015918612481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.442 × 10¹⁰⁰(101-digit number)

14420089706341369122…24634562031837224961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.884 × 10¹⁰⁰(101-digit number)

28840179412682738245…49269124063674449921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.768 × 10¹⁰⁰(101-digit number)

57680358825365476491…98538248127348899841

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 #513,420

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