Block #114,568

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/13/2013, 5:40:52 AM · Difficulty 9.7399 · 6,712,375 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

12cbbec47b670d4b15d48d507770be127dc20f5865a63a1cdfd6a049b0694642

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Height

#114,568

Difficulty

9.739872

Transactions

Size

201 B

Version

Bits

09bd6846

Nonce

44,076

Timestamp

8/13/2013, 5:40:52 AM

Confirmations

6,712,375

Mined by

⛏️ P2SHANLKLSDrvj3WK51nAjjHkkPSvFyECYyy1Z

Merkle Root

aa4b9dfe2e0987112f1eb045347810479da18106410b1e88d2aa01bb9d4ddf0d

Transactions (1)

Coinbaseaa4b9dfe2e0987…aa01bb9d4ddf0d

1 in → 1 out10.5300 XPM109 B

ANLKLSDr…yECYyy1Z

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.

2.991 × 10⁹⁸(99-digit number)

29917747961459402561…96092620235839505849

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

2.991 × 10⁹⁸(99-digit number)

29917747961459402561…96092620235839505849

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.983 × 10⁹⁸(99-digit number)

59835495922918805122…92185240471679011699

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.196 × 10⁹⁹(100-digit number)

11967099184583761024…84370480943358023399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.393 × 10⁹⁹(100-digit number)

23934198369167522049…68740961886716046799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.786 × 10⁹⁹(100-digit number)

47868396738335044098…37481923773432093599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.573 × 10⁹⁹(100-digit number)

95736793476670088196…74963847546864187199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.914 × 10¹⁰⁰(101-digit number)

19147358695334017639…49927695093728374399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.829 × 10¹⁰⁰(101-digit number)

38294717390668035278…99855390187456748799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.658 × 10¹⁰⁰(101-digit number)

76589434781336070556…99710780374913497599

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 #114,568

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