Block #79,637

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/23/2013, 3:09:21 PM · Difficulty 9.2447 · 6,712,349 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

872b57802d46191045cc0af46d085dcde49b49db360b176d1ee25833d2303543

View on Chainz ↗

Height

#79,637

Difficulty

9.244709

Transactions

Size

1.15 KB

Version

Bits

093ea542

Nonce

932

Timestamp

7/23/2013, 3:09:21 PM

Confirmations

6,712,349

Merkle Root

3a678bfb8e23c53565abee3eef081a2b18cb86affcbe981fd5b8ef06caed9b9c

Transactions (2)

Coinbased00db03da8fdaa…c7080473533ac7

1 in → 1 out11.6900 XPM110 B

AMvtMYgm…o2vhrUAm

e247b14d540991…4b8f836b58ebb9

6 in → 2 out47.9878 XPM967 B

AFwfgFgx…QviYCTp2 APbyemm8…wirf3pUh

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.

1.377 × 10¹¹¹(112-digit number)

13770772952995638705…03571007712818453281

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

1.377 × 10¹¹¹(112-digit number)

13770772952995638705…03571007712818453281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.754 × 10¹¹¹(112-digit number)

27541545905991277411…07142015425636906561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.508 × 10¹¹¹(112-digit number)

55083091811982554822…14284030851273813121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.101 × 10¹¹²(113-digit number)

11016618362396510964…28568061702547626241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.203 × 10¹¹²(113-digit number)

22033236724793021929…57136123405095252481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.406 × 10¹¹²(113-digit number)

44066473449586043858…14272246810190504961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.813 × 10¹¹²(113-digit number)

88132946899172087716…28544493620381009921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.762 × 10¹¹³(114-digit number)

17626589379834417543…57088987240762019841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.525 × 10¹¹³(114-digit number)

35253178759668835086…14177974481524039681

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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