Block #99,310

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/5/2013, 3:25:09 PM · Difficulty 9.3816 · 6,716,619 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0ffade5f9e9660fd0c6c6a596c80442ccc69a88afae48cd2627c463fa896b854

View on Chainz ↗

Height

#99,310

Difficulty

9.381600

Transactions

Size

818 B

Version

Bits

0961b082

Nonce

33,917

Timestamp

8/5/2013, 3:25:09 PM

Confirmations

6,716,619

Mined by

⛏️ P2SHAWNSGYZjPRyyM73fYFzfBXaPQXcvAknq2C

Merkle Root

250cfa383ebba79498f3216d383f16b89e7130fbf8c5e2e79b3133962ee30a00

Transactions (2)

Coinbase15ee404685a5d5…7d75913bc7054d

1 in → 1 out11.3600 XPM109 B

AWNSGYZj…cvAknq2C

a2bab52940154d…255e32cc91b8ac

5 in → 1 out58.5400 XPM614 B

AVwR4LZz…56CfV3Xr

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.

2.365 × 10¹⁰⁷(108-digit number)

23652233767649489756…61841337457460570959

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

2.365 × 10¹⁰⁷(108-digit number)

23652233767649489756…61841337457460570959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.730 × 10¹⁰⁷(108-digit number)

47304467535298979513…23682674914921141919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.460 × 10¹⁰⁷(108-digit number)

94608935070597959027…47365349829842283839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.892 × 10¹⁰⁸(109-digit number)

18921787014119591805…94730699659684567679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.784 × 10¹⁰⁸(109-digit number)

37843574028239183611…89461399319369135359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.568 × 10¹⁰⁸(109-digit number)

75687148056478367222…78922798638738270719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.513 × 10¹⁰⁹(110-digit number)

15137429611295673444…57845597277476541439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.027 × 10¹⁰⁹(110-digit number)

30274859222591346888…15691194554953082879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.054 × 10¹⁰⁹(110-digit number)

60549718445182693777…31382389109906165759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer

Block #99,310

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