Block #53,502

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 3:40:36 PM · Difficulty 8.9242 · 6,741,851 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f4e8a3402f928f59a938c7e76eea0e01f4787ed2421604c31822b90e2f8c45b0

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Height

#53,502

Difficulty

8.924192

Transactions

Size

205 B

Version

Bits

08ec97d7

Nonce

Timestamp

7/16/2013, 3:40:36 PM

Confirmations

6,741,851

Mined by

⛏️ P2SHAeTcmmqHMYEKBSfvTp4dmwQ4JaLrFchfe1

Merkle Root

03d9b21dcbad65e4184cc15ccd70b03f25ca881b88f15b2a37377733a66a323c

Transactions (1)

Coinbase03d9b21dcbad65…377733a66a323c

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.

2.459 × 10¹⁰⁷(108-digit number)

24590843449773588003…22207410049688286721

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

2.459 × 10¹⁰⁷(108-digit number)

24590843449773588003…22207410049688286721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.918 × 10¹⁰⁷(108-digit number)

49181686899547176007…44414820099376573441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.836 × 10¹⁰⁷(108-digit number)

98363373799094352015…88829640198753146881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.967 × 10¹⁰⁸(109-digit number)

19672674759818870403…77659280397506293761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.934 × 10¹⁰⁸(109-digit number)

39345349519637740806…55318560795012587521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.869 × 10¹⁰⁸(109-digit number)

78690699039275481612…10637121590025175041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.573 × 10¹⁰⁹(110-digit number)

15738139807855096322…21274243180050350081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.147 × 10¹⁰⁹(110-digit number)

31476279615710192645…42548486360100700161

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