Block #26,510

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 5:37:56 AM · Difficulty 7.9755 · 6,768,068 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7a5d7b7aebfcc6fb382ec320fd899c49ac6959ca061e413734bfbbfbc7c1bd6f

View on Chainz ↗

Height

#26,510

Difficulty

7.975453

Transactions

Size

890 B

Version

Bits

07f9b746

Nonce

805

Timestamp

7/13/2013, 5:37:56 AM

Confirmations

6,768,068

Mined by

⛏️ P2SHAZC3EnRQXBknjURZ7pF3PdWcPWFfJNWhuw

Merkle Root

0acb3e019ed5a5432614b7ee221407258c031d094ce1cb9d6579bcf4af7c51cd

Transactions (3)

Coinbase2bd7d84e75d5f9…470945fd6de091

1 in → 1 out15.7200 XPM108 B

AZC3EnRQ…FfJNWhuw

e1840106805dd4…0e081ca53e1c97

2 in → 1 out31.7000 XPM274 B

AZtCX4LT…teQvXwUK

3244b73abd61a7…09ad34439a9af6

2 in → 3 out1.6962 XPM407 B

Aa9WE6sk…RxE6LMZ4 AKkuHem8…KecFMdXR ARJkzra6…SxjEuMgW

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.

1.510 × 10¹²²(123-digit number)

15108231300271678698…14518098829815769501

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

1.510 × 10¹²²(123-digit number)

15108231300271678698…14518098829815769501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.021 × 10¹²²(123-digit number)

30216462600543357396…29036197659631539001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.043 × 10¹²²(123-digit number)

60432925201086714793…58072395319263078001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.208 × 10¹²³(124-digit number)

12086585040217342958…16144790638526156001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.417 × 10¹²³(124-digit number)

24173170080434685917…32289581277052312001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.834 × 10¹²³(124-digit number)

48346340160869371835…64579162554104624001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.669 × 10¹²³(124-digit number)

96692680321738743670…29158325108209248001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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