Block #25,945

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/13/2013, 3:47:56 AM · Difficulty 7.9731 · 6,763,837 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

21c4289bf3df529b99c546015784da764239b9eef3f2388115f05d2eac33a778

View on Chainz ↗

Height

#25,945

Difficulty

7.973116

Transactions

Size

198 B

Version

Bits

07f91e1f

Nonce

159

Timestamp

7/13/2013, 3:47:56 AM

Confirmations

6,763,837

Merkle Root

5513729d7cf0b720a533258ad0485c06e55b482dcc6a677788ef9fddf3501f79

Transactions (1)

Coinbase5513729d7cf0b7…ef9fddf3501f79

1 in → 1 out15.7100 XPM109 B

AYaFX8TY…VjRNmAju

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.

6.625 × 10⁹¹(92-digit number)

66257396466383573651…11405254661716921519

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

6.625 × 10⁹¹(92-digit number)

66257396466383573651…11405254661716921519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.325 × 10⁹²(93-digit number)

13251479293276714730…22810509323433843039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.650 × 10⁹²(93-digit number)

26502958586553429460…45621018646867686079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.300 × 10⁹²(93-digit number)

53005917173106858921…91242037293735372159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.060 × 10⁹³(94-digit number)

10601183434621371784…82484074587470744319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.120 × 10⁹³(94-digit number)

21202366869242743568…64968149174941488639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.240 × 10⁹³(94-digit number)

42404733738485487136…29936298349882977279

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer