Block #172,412

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/20/2013, 5:55:34 AM · Difficulty 9.8619 · 6,620,285 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

8fefa0f97db4ef7af080cf5f642d24753736f29cff2457ff01149fdae9cb6f1c

View on Chainz ↗

Height

#172,412

Difficulty

9.861915

Transactions

Size

199 B

Version

Bits

09dca672

Nonce

398,120

Timestamp

9/20/2013, 5:55:34 AM

Confirmations

6,620,285

Merkle Root

542f2035ed78beb6bbc0ea234590d052919b4ab1903bd7bf95de1bbc89a3cdf8

Transactions (1)

Coinbase542f2035ed78be…de1bbc89a3cdf8

1 in → 1 out10.2700 XPM109 B

AP91QEDQ…W6JZAB9n

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.

2.929 × 10⁹⁵(96-digit number)

29299030625690674694…18159971130946159361

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

2.929 × 10⁹⁵(96-digit number)

29299030625690674694…18159971130946159361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.859 × 10⁹⁵(96-digit number)

58598061251381349389…36319942261892318721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.171 × 10⁹⁶(97-digit number)

11719612250276269877…72639884523784637441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.343 × 10⁹⁶(97-digit number)

23439224500552539755…45279769047569274881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.687 × 10⁹⁶(97-digit number)

46878449001105079511…90559538095138549761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.375 × 10⁹⁶(97-digit number)

93756898002210159023…81119076190277099521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.875 × 10⁹⁷(98-digit number)

18751379600442031804…62238152380554199041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.750 × 10⁹⁷(98-digit number)

37502759200884063609…24476304761108398081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.500 × 10⁹⁷(98-digit number)

75005518401768127218…48952609522216796161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.500 × 10⁹⁸(99-digit number)

15001103680353625443…97905219044433592321

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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