Block #476,024

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/5/2014, 2:04:34 PM · Difficulty 10.4673 · 6,329,766 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6fe0f5adb46749c730531e97ff37020d173c4eae2bbe0c06c4c4b57cc9551398

View on Chainz ↗

Height

#476,024

Difficulty

10.467303

Transactions

Size

934 B

Version

Bits

0a77a12b

Nonce

211,307

Timestamp

4/5/2014, 2:04:34 PM

Confirmations

6,329,766

Mined by

⛏️ xCaS@AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b2d8b214d69b43ec99544eccde4f0fdab65f6ef9ac89afbe6aa17317e79505eb

Transactions (1)

Coinbaseb2d8b214d69b43…a17317e79505eb

1 in → 23 out9.1100 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1

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.

1.672 × 10⁹²(93-digit number)

16726430647220236891…19013617124571368201

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

1.672 × 10⁹²(93-digit number)

16726430647220236891…19013617124571368201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.345 × 10⁹²(93-digit number)

33452861294440473782…38027234249142736401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.690 × 10⁹²(93-digit number)

66905722588880947564…76054468498285472801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.338 × 10⁹³(94-digit number)

13381144517776189512…52108936996570945601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.676 × 10⁹³(94-digit number)

26762289035552379025…04217873993141891201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.352 × 10⁹³(94-digit number)

53524578071104758051…08435747986283782401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.070 × 10⁹⁴(95-digit number)

10704915614220951610…16871495972567564801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.140 × 10⁹⁴(95-digit number)

21409831228441903220…33742991945135129601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.281 × 10⁹⁴(95-digit number)

42819662456883806441…67485983890270259201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.563 × 10⁹⁴(95-digit number)

85639324913767612882…34971967780540518401

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