Block #289,394

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/2/2013, 4:30:26 AM · Difficulty 9.9885 · 6,510,094 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

81ac070e845a415da96105c08f1ac21c3ba35645cf5a1f5b3fb20f0d1b1c8ed8

View on Chainz ↗

Height

#289,394

Difficulty

9.988491

Transactions

Size

1.21 KB

Version

Bits

09fd0dbf

Nonce

403,387

Timestamp

12/2/2013, 4:30:26 AM

Confirmations

6,510,094

Mined by

⛏️ rjaRAN63YyQR2Qj7epgahxFKAKwLXt1tfe566A

Merkle Root

73ce9a9210922ed2b6a1c1c263fae7f27e92f4f6294ab44356688f9b81f4a4c8

Transactions (1)

Coinbase73ce9a9210922e…688f9b81f4a4c8

1 in → 32 out9.9900 XPM1.12 KB

AN63YyQR…1tfe566A AYcLTeXR…bscgPops AZninDSu…FvgDMwC4 ARskhKeb…UgDvvX9P AU6BArRg…BhwbqmiH

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.

1.052 × 10⁹⁸(99-digit number)

10524302612274955796…27873869387070345601

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

1.052 × 10⁹⁸(99-digit number)

10524302612274955796…27873869387070345601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.104 × 10⁹⁸(99-digit number)

21048605224549911592…55747738774140691201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.209 × 10⁹⁸(99-digit number)

42097210449099823184…11495477548281382401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.419 × 10⁹⁸(99-digit number)

84194420898199646369…22990955096562764801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.683 × 10⁹⁹(100-digit number)

16838884179639929273…45981910193125529601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.367 × 10⁹⁹(100-digit number)

33677768359279858547…91963820386251059201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.735 × 10⁹⁹(100-digit number)

67355536718559717095…83927640772502118401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.347 × 10¹⁰⁰(101-digit number)

13471107343711943419…67855281545004236801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.694 × 10¹⁰⁰(101-digit number)

26942214687423886838…35710563090008473601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.388 × 10¹⁰⁰(101-digit number)

53884429374847773676…71421126180016947201

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