Block #285,575

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/30/2013, 1:16:49 PM · Difficulty 9.9845 · 6,517,125 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7029ff9f940d726059cc8b2afe50d96f0a03ca68acc3843d25be3e45a33ae6a2

View on Chainz ↗

Height

#285,575

Difficulty

9.984490

Transactions

Size

1005 B

Version

Bits

09fc078c

Nonce

13,463

Timestamp

11/30/2013, 1:16:49 PM

Confirmations

6,517,125

Mined by

⛏️ aRJJAVss9H5FkXhhqqTXyhqhrXDK3UzXhyMijY

Merkle Root

5c89005db05e225c58ee40a98efaa57222801e1f25a545e8b4b6156652d1d7da

Transactions (1)

Coinbase5c89005db05e22…b6156652d1d7da

1 in → 25 out10.0200 XPM913 B

AVss9H5F…zXhyMijY APeshfYV…3PKcKMKH AbtgNzNb…9Atvu81w AeFawUfC…dps5LLeM Acs9SHrk…QJSB8SFG

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.

4.806 × 10⁹⁸(99-digit number)

48061570303218016333…17116735825373470721

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

4.806 × 10⁹⁸(99-digit number)

48061570303218016333…17116735825373470721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.612 × 10⁹⁸(99-digit number)

96123140606436032667…34233471650746941441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.922 × 10⁹⁹(100-digit number)

19224628121287206533…68466943301493882881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.844 × 10⁹⁹(100-digit number)

38449256242574413067…36933886602987765761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.689 × 10⁹⁹(100-digit number)

76898512485148826134…73867773205975531521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.537 × 10¹⁰⁰(101-digit number)

15379702497029765226…47735546411951063041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.075 × 10¹⁰⁰(101-digit number)

30759404994059530453…95471092823902126081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.151 × 10¹⁰⁰(101-digit number)

61518809988119060907…90942185647804252161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.230 × 10¹⁰¹(102-digit number)

12303761997623812181…81884371295608504321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.460 × 10¹⁰¹(102-digit number)

24607523995247624362…63768742591217008641

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