Block #53,336

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 2:49:17 PM · Difficulty 8.9224 · 6,736,719 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

1cbc3ebd12b2ab2de518e2398131935505e6481b5cc436ef4cb68c9ca9974024

View on Chainz ↗

Height

#53,336

Difficulty

8.922442

Transactions

Size

199 B

Version

Bits

08ec252b

Nonce

147

Timestamp

7/16/2013, 2:49:17 PM

Confirmations

6,736,719

Merkle Root

571f3b3f80229c304350ee4d89d6360f822350caeb66d8b066f348b7433701cb

Transactions (1)

Coinbase571f3b3f80229c…f348b7433701cb

1 in → 1 out12.5400 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.

1.632 × 10⁹³(94-digit number)

16321211211952785092…89529947806664198741

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

1.632 × 10⁹³(94-digit number)

16321211211952785092…89529947806664198741

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.264 × 10⁹³(94-digit number)

32642422423905570185…79059895613328397481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.528 × 10⁹³(94-digit number)

65284844847811140370…58119791226656794961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.305 × 10⁹⁴(95-digit number)

13056968969562228074…16239582453313589921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.611 × 10⁹⁴(95-digit number)

26113937939124456148…32479164906627179841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.222 × 10⁹⁴(95-digit number)

52227875878248912296…64958329813254359681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.044 × 10⁹⁵(96-digit number)

10445575175649782459…29916659626508719361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.089 × 10⁹⁵(96-digit number)

20891150351299564918…59833319253017438721

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