Block #52,320

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 9:47:39 AM · Difficulty 8.9106 · 6,739,295 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9a31d9184d805992d18a018fffe0008bbcb56713268c0df6d9a32cf75b3849f5

View on Chainz ↗

Height

#52,320

Difficulty

8.910602

Transactions

Size

197 B

Version

Bits

08e91d32

Nonce

1,411

Timestamp

7/16/2013, 9:47:39 AM

Confirmations

6,739,295

Merkle Root

d8c66555d10debbf911b13fd3cd6caa48afaf2bf9321aa2854fa946cf259a3e3

Transactions (1)

Coinbased8c66555d10deb…fa946cf259a3e3

1 in → 1 out12.5800 XPM110 B

AeTcmmqH…LrFchfe1

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.

9.320 × 10⁸⁶(87-digit number)

93207257109430496694…72780141924241017601

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

9.320 × 10⁸⁶(87-digit number)

93207257109430496694…72780141924241017601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.864 × 10⁸⁷(88-digit number)

18641451421886099338…45560283848482035201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.728 × 10⁸⁷(88-digit number)

37282902843772198677…91120567696964070401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.456 × 10⁸⁷(88-digit number)

74565805687544397355…82241135393928140801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.491 × 10⁸⁸(89-digit number)

14913161137508879471…64482270787856281601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.982 × 10⁸⁸(89-digit number)

29826322275017758942…28964541575712563201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.965 × 10⁸⁸(89-digit number)

59652644550035517884…57929083151425126401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.193 × 10⁸⁹(90-digit number)

11930528910007103576…15858166302850252801

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