Block #287,341

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/1/2013, 6:59:29 AM · Difficulty 9.9866 · 6,544,050 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

14604bd7a230c4fc424a5329e18ba778190c4463402fee1218292e51574dad64

View on Chainz ↗

Height

#287,341

Difficulty

9.986561

Transactions

Size

1.04 KB

Version

Bits

09fc8f4a

Nonce

17,906

Timestamp

12/1/2013, 6:59:29 AM

Confirmations

6,544,050

Mined by

⛏️ mbaRAUW89vJdF6ijDPLwFez7o1o2WYBiczGLRw

Merkle Root

1808f018eee40bb485440658b72ab056923b171e15a34170ec68bf611a4c4f33

Transactions (1)

Coinbase1808f018eee40b…68bf611a4c4f33

1 in → 27 out10.0100 XPM981 B

AUW89vJd…BiczGLRw AYrgZtF4…6oLCC7XK AY6MvLfB…Z3ZLcoYn AJj92cB9…AX3cvzBm AKde1i4d…88R1bw6g

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.

6.265 × 10⁸⁸(89-digit number)

62652550880642779816…83749275137123722521

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

6.265 × 10⁸⁸(89-digit number)

62652550880642779816…83749275137123722521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.253 × 10⁸⁹(90-digit number)

12530510176128555963…67498550274247445041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.506 × 10⁸⁹(90-digit number)

25061020352257111926…34997100548494890081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.012 × 10⁸⁹(90-digit number)

50122040704514223853…69994201096989780161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.002 × 10⁹⁰(91-digit number)

10024408140902844770…39988402193979560321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.004 × 10⁹⁰(91-digit number)

20048816281805689541…79976804387959120641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.009 × 10⁹⁰(91-digit number)

40097632563611379082…59953608775918241281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.019 × 10⁹⁰(91-digit number)

80195265127222758165…19907217551836482561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.603 × 10⁹¹(92-digit number)

16039053025444551633…39814435103672965121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.207 × 10⁹¹(92-digit number)

32078106050889103266…79628870207345930241

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

Block #287,341

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