Block #402,571

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/13/2014, 12:56:31 PM · Difficulty 10.4371 · 6,401,219 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2b23d8cc8a166eab6ff75d20b88ebbf660dedd0afe95bba096e4ce8fb633864b

View on Chainz ↗

Height

#402,571

Difficulty

10.437105

Transactions

Size

834 B

Version

Bits

0a6fe620

Nonce

5,787

Timestamp

2/13/2014, 12:56:31 PM

Confirmations

6,401,219

Mined by

⛏️ $aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3a48e45648a0b8e6a33cbcaaa5210aaa410306e2005b32eee8f7fa9515cd4a56

Transactions (1)

Coinbase3a48e45648a0b8…f7fa9515cd4a56

1 in → 20 out9.1700 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AXX1wTMN…FfSE8V61 AXmS7tZu…11YypHLP

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.

2.820 × 10⁹⁶(97-digit number)

28207357208211027083…30441082264900793601

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

2.820 × 10⁹⁶(97-digit number)

28207357208211027083…30441082264900793601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.641 × 10⁹⁶(97-digit number)

56414714416422054166…60882164529801587201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.128 × 10⁹⁷(98-digit number)

11282942883284410833…21764329059603174401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.256 × 10⁹⁷(98-digit number)

22565885766568821666…43528658119206348801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.513 × 10⁹⁷(98-digit number)

45131771533137643333…87057316238412697601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.026 × 10⁹⁷(98-digit number)

90263543066275286666…74114632476825395201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.805 × 10⁹⁸(99-digit number)

18052708613255057333…48229264953650790401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.610 × 10⁹⁸(99-digit number)

36105417226510114666…96458529907301580801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.221 × 10⁹⁸(99-digit number)

72210834453020229333…92917059814603161601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.444 × 10⁹⁹(100-digit number)

14442166890604045866…85834119629206323201

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