Block #288,672

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/1/2013, 8:47:24 PM · Difficulty 9.9879 · 6,507,762 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0da619258d185f60ba6ac4dfb2b32e6bedc401e73ed07c45bf0fcd28ab6ff068

View on Chainz ↗

Height

#288,672

Difficulty

9.987880

Transactions

Size

985 B

Version

Bits

09fce5b6

Nonce

9,302

Timestamp

12/1/2013, 8:47:24 PM

Confirmations

6,507,762

Mined by

⛏️ P2SHAYmfScSwoFfsio4f8erjWNjUdUtRbHYjni

Merkle Root

fe69047d263fa74c88726098676a4ca68c22850a0c3827688a53d2e548d7e4f7

Transactions (2)

Coinbase245f84ccba5418…12142c029b3850

1 in → 1 out10.0200 XPM110 B

AYmfScSw…tRbHYjni

7cd3b1c2565ee9…f8613b1b654977

5 in → 1 out1.3628 XPM784 B

AJtCDakk…cmy9cKRa

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.

5.865 × 10⁹⁷(98-digit number)

58650800808574526915…19248275560629196801

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

5.865 × 10⁹⁷(98-digit number)

58650800808574526915…19248275560629196801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.173 × 10⁹⁸(99-digit number)

11730160161714905383…38496551121258393601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.346 × 10⁹⁸(99-digit number)

23460320323429810766…76993102242516787201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.692 × 10⁹⁸(99-digit number)

46920640646859621532…53986204485033574401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.384 × 10⁹⁸(99-digit number)

93841281293719243065…07972408970067148801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.876 × 10⁹⁹(100-digit number)

18768256258743848613…15944817940134297601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.753 × 10⁹⁹(100-digit number)

37536512517487697226…31889635880268595201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.507 × 10⁹⁹(100-digit number)

75073025034975394452…63779271760537190401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.501 × 10¹⁰⁰(101-digit number)

15014605006995078890…27558543521074380801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.002 × 10¹⁰⁰(101-digit number)

30029210013990157780…55117087042148761601

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