Block #270,529

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/24/2013, 12:35:17 AM · Difficulty 9.9516 · 6,535,307 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c3530e193a52ce45be1a05bc2438bdfc102315c09888df903435517efbf61557

View on Chainz ↗

Height

#270,529

Difficulty

9.951643

Transactions

Size

1.94 KB

Version

Bits

09f39ede

Nonce

588,495

Timestamp

11/24/2013, 12:35:17 AM

Confirmations

6,535,307

Mined by

⛏️ aRIAPZy8y6EJuYdTXF8qsqDMcghECQZaGQjfp

Merkle Root

122d39f74317052bb178586555b6696cbfbb53746ebe56595510c3a4c7366f49

Transactions (1)

Coinbase122d39f7431705…10c3a4c7366f49

1 in → 54 out10.0600 XPM1.85 KB

APZy8y6E…QZaGQjfp AdnG9gQ7…N9B7mA2p AHTTUHKB…g8V7VRLq AVzhvfTX…ZzNJYq61 AWZd1qVJ…9pj9yfPa

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.

1.842 × 10⁹⁷(98-digit number)

18424380372322887994…78733396338142531521

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

1.842 × 10⁹⁷(98-digit number)

18424380372322887994…78733396338142531521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.684 × 10⁹⁷(98-digit number)

36848760744645775988…57466792676285063041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.369 × 10⁹⁷(98-digit number)

73697521489291551977…14933585352570126081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.473 × 10⁹⁸(99-digit number)

14739504297858310395…29867170705140252161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.947 × 10⁹⁸(99-digit number)

29479008595716620791…59734341410280504321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.895 × 10⁹⁸(99-digit number)

58958017191433241582…19468682820561008641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.179 × 10⁹⁹(100-digit number)

11791603438286648316…38937365641122017281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.358 × 10⁹⁹(100-digit number)

23583206876573296632…77874731282244034561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.716 × 10⁹⁹(100-digit number)

47166413753146593265…55749462564488069121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

9.433 × 10⁹⁹(100-digit number)

94332827506293186531…11498925128976138241

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