Block #171,424

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/19/2013, 11:55:38 AM · Difficulty 9.8643 · 6,621,418 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

8c7961ed191806144a4a53afbf20e33d171f1ee11fda714e105f1ea808a35e0b

View on Chainz ↗

Height

#171,424

Difficulty

9.864266

Transactions

Size

198 B

Version

Bits

09dd4091

Nonce

74,879

Timestamp

9/19/2013, 11:55:38 AM

Confirmations

6,621,418

Merkle Root

df592c1f5edfc0977536aba77fd40de54e123d9d0fd74525254ce373984209f4

Transactions (1)

Coinbasedf592c1f5edfc0…4ce373984209f4

1 in → 1 out10.2600 XPM109 B

AKnjzMcH…jxdaXcap

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.

1.395 × 10⁹³(94-digit number)

13957402438267260438…31405017773988403201

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

1.395 × 10⁹³(94-digit number)

13957402438267260438…31405017773988403201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.791 × 10⁹³(94-digit number)

27914804876534520877…62810035547976806401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.582 × 10⁹³(94-digit number)

55829609753069041755…25620071095953612801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.116 × 10⁹⁴(95-digit number)

11165921950613808351…51240142191907225601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.233 × 10⁹⁴(95-digit number)

22331843901227616702…02480284383814451201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.466 × 10⁹⁴(95-digit number)

44663687802455233404…04960568767628902401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.932 × 10⁹⁴(95-digit number)

89327375604910466809…09921137535257804801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.786 × 10⁹⁵(96-digit number)

17865475120982093361…19842275070515609601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.573 × 10⁹⁵(96-digit number)

35730950241964186723…39684550141031219201

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