Block #213,286

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/16/2013, 7:16:29 PM · Difficulty 9.9209 · 6,579,272 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

04cdb985a31927b161fd4c147f6fb7047b79531399b9ca1784d7822d09735d14

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Height

#213,286

Difficulty

9.920860

Transactions

Size

198 B

Version

Bits

09ebbd83

Nonce

63,484

Timestamp

10/16/2013, 7:16:29 PM

Confirmations

6,579,272

Merkle Root

f10e755e67bd540605d5d2348e3237da6751e11b52f4e3775c720446b84c0841

Transactions (1)

Coinbasef10e755e67bd54…720446b84c0841

1 in → 1 out10.1500 XPM109 B

AK9vVy2j…niNoc5U8

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.

2.429 × 10⁹¹(92-digit number)

24293598495777173911…00111879236591309001

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

2.429 × 10⁹¹(92-digit number)

24293598495777173911…00111879236591309001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.858 × 10⁹¹(92-digit number)

48587196991554347822…00223758473182618001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.717 × 10⁹¹(92-digit number)

97174393983108695644…00447516946365236001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.943 × 10⁹²(93-digit number)

19434878796621739128…00895033892730472001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.886 × 10⁹²(93-digit number)

38869757593243478257…01790067785460944001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.773 × 10⁹²(93-digit number)

77739515186486956515…03580135570921888001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.554 × 10⁹³(94-digit number)

15547903037297391303…07160271141843776001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.109 × 10⁹³(94-digit number)

31095806074594782606…14320542283687552001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.219 × 10⁹³(94-digit number)

62191612149189565212…28641084567375104001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.243 × 10⁹⁴(95-digit number)

12438322429837913042…57282169134750208001

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