Block #59,482

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 2:28:53 AM · Difficulty 8.9651 · 6,756,553 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

cce3f559b720d639b9ca50ad97f26ff967fe4bd498314ed7cbbeea8c88f6dc72

View on Chainz ↗

Height

#59,482

Difficulty

8.965105

Transactions

Size

692 B

Version

Bits

08f71119

Nonce

285

Timestamp

7/18/2013, 2:28:53 AM

Confirmations

6,756,553

Mined by

⛏️ P2SHAPBGTBJfRLxyEV5iYiRnp2o8AhY9gCcZLa

Merkle Root

7b0fe3d316670b6712ef98408c2e3e07f3e77e11c448f165b93be0a96de02ba9

Transactions (2)

Coinbase941665452eac9a…fe735ed02259e7

1 in → 1 out12.4300 XPM110 B

APBGTBJf…Y9gCcZLa

f4c384b6f9cf92…1ac1b6e2d512f4

3 in → 1 out299.9000 XPM488 B

AMKxJqj9…CM2SJHqp

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.

1.477 × 10¹⁰³(104-digit number)

14770737627893255584…91209932192567397921

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

1.477 × 10¹⁰³(104-digit number)

14770737627893255584…91209932192567397921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.954 × 10¹⁰³(104-digit number)

29541475255786511168…82419864385134795841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.908 × 10¹⁰³(104-digit number)

59082950511573022337…64839728770269591681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.181 × 10¹⁰⁴(105-digit number)

11816590102314604467…29679457540539183361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.363 × 10¹⁰⁴(105-digit number)

23633180204629208934…59358915081078366721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.726 × 10¹⁰⁴(105-digit number)

47266360409258417869…18717830162156733441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.453 × 10¹⁰⁴(105-digit number)

94532720818516835739…37435660324313466881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.890 × 10¹⁰⁵(106-digit number)

18906544163703367147…74871320648626933761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.781 × 10¹⁰⁵(106-digit number)

37813088327406734295…49742641297253867521

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

Block #59,482

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