Block #53,432

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 3:20:51 PM · Difficulty 8.9234 · 6,756,493 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f06e1caa9c3bcd9fd411bcbdb9c3779410d3301784078702eebe756d6dc669fe

View on Chainz ↗

Height

#53,432

Difficulty

8.923430

Transactions

Size

205 B

Version

Bits

08ec65ec

Nonce

519

Timestamp

7/16/2013, 3:20:51 PM

Confirmations

6,756,493

Mined by

⛏️ P2SHAJbRF9Vh3Pm1qDnFdVGkh4jvYocmDMZyVK

Merkle Root

3f2099f625fbfc8b34ad64afbc40913c65c5bd65cc6cc7d30796b1de0ee2a68f

Transactions (1)

Coinbase3f2099f625fbfc…96b1de0ee2a68f

1 in → 1 out12.5400 XPM109 B

AJbRF9Vh…cmDMZyVK

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.

2.740 × 10¹⁰⁹(110-digit number)

27407483660928377494…74217899929555878801

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

2.740 × 10¹⁰⁹(110-digit number)

27407483660928377494…74217899929555878801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.481 × 10¹⁰⁹(110-digit number)

54814967321856754989…48435799859111757601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.096 × 10¹¹⁰(111-digit number)

10962993464371350997…96871599718223515201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.192 × 10¹¹⁰(111-digit number)

21925986928742701995…93743199436447030401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.385 × 10¹¹⁰(111-digit number)

43851973857485403991…87486398872894060801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.770 × 10¹¹⁰(111-digit number)

87703947714970807983…74972797745788121601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.754 × 10¹¹¹(112-digit number)

17540789542994161596…49945595491576243201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.508 × 10¹¹¹(112-digit number)

35081579085988323193…99891190983152486401

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #53,432

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