Block #495,188

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/16/2014, 12:47:01 PM · Difficulty 10.7321 · 6,303,632 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

66f1a78e3a43b8e02452107e5b33638cf0cc6d6b4ce89597c450fce80fe93428

View on Chainz ↗

Height

#495,188

Difficulty

10.732094

Transactions

Size

731 B

Version

Bits

0abb6a86

Nonce

210,511

Timestamp

4/16/2014, 12:47:01 PM

Confirmations

6,303,632

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

21337a07fccb548613439346a9b833eb8dbc3f6d8ee50018259b93e41f648161

Transactions (2)

Coinbasedda80b540482d5…39c8b6da242df0

1 in → 1 out8.6800 XPM116 B

AbwWkWZt…kawDhufa

6adea91eafc2c0…52ca4ca5e393a3

3 in → 2 out15.9129 XPM524 B

AVqQ8PPb…y5xghjGM AMSxM3FP…eM55gXEt

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.

1.955 × 10⁹⁶(97-digit number)

19552445936398989820…63010261325151479921

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

1.955 × 10⁹⁶(97-digit number)

19552445936398989820…63010261325151479921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.910 × 10⁹⁶(97-digit number)

39104891872797979640…26020522650302959841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.820 × 10⁹⁶(97-digit number)

78209783745595959281…52041045300605919681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.564 × 10⁹⁷(98-digit number)

15641956749119191856…04082090601211839361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.128 × 10⁹⁷(98-digit number)

31283913498238383712…08164181202423678721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.256 × 10⁹⁷(98-digit number)

62567826996476767425…16328362404847357441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.251 × 10⁹⁸(99-digit number)

12513565399295353485…32656724809694714881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.502 × 10⁹⁸(99-digit number)

25027130798590706970…65313449619389429761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.005 × 10⁹⁸(99-digit number)

50054261597181413940…30626899238778859521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.001 × 10⁹⁹(100-digit number)

10010852319436282788…61253798477557719041

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