Block #263,950

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/18/2013, 6:33:39 AM · Difficulty 9.9653 · 6,539,656 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

05b1998440c6c3c7850ce6c6feb30a36fde9d339bc09dcac0a4cfff2696df5e7

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Height

#263,950

Difficulty

9.965276

Transactions

Size

2.21 KB

Version

Bits

09f71c59

Nonce

115,424

Timestamp

11/18/2013, 6:33:39 AM

Confirmations

6,539,656

Mined by

⛏️ aRARskhKebzwhUsQms8dTj78qtmaUgDvvX9P

Merkle Root

c53138a6e44068a429c6211f24326c45bbad897bf821b99f077863a7b4de4aad

Transactions (1)

Coinbasec53138a6e44068…7863a7b4de4aad

1 in → 62 out10.0200 XPM2.12 KB

ARskhKeb…UgDvvX9P AFqKfjez…qX9Ace3g AdnG9gQ7…N9B7mA2p Ae7UyoY4…DtgAv9cY AQapNBe8…Pxk4vkev

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.

5.781 × 10⁸⁹(90-digit number)

57816510611085614008…01453529571559789121

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

5.781 × 10⁸⁹(90-digit number)

57816510611085614008…01453529571559789121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.156 × 10⁹⁰(91-digit number)

11563302122217122801…02907059143119578241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.312 × 10⁹⁰(91-digit number)

23126604244434245603…05814118286239156481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.625 × 10⁹⁰(91-digit number)

46253208488868491206…11628236572478312961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.250 × 10⁹⁰(91-digit number)

92506416977736982413…23256473144956625921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.850 × 10⁹¹(92-digit number)

18501283395547396482…46512946289913251841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.700 × 10⁹¹(92-digit number)

37002566791094792965…93025892579826503681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.400 × 10⁹¹(92-digit number)

74005133582189585930…86051785159653007361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.480 × 10⁹²(93-digit number)

14801026716437917186…72103570319306014721

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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