Block #234,855

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/30/2013, 2:08:55 PM · Difficulty 9.9448 · 6,564,153 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8761c091bc5286c28cb5faed01a07584e0ec9f31594ee530f0a9bb70590275d5

View on Chainz ↗

Height

#234,855

Difficulty

9.944784

Transactions

Size

1.57 KB

Version

Bits

09f1dd57

Nonce

298,391

Timestamp

10/30/2013, 2:08:55 PM

Confirmations

6,564,153

Mined by

⛏️ gRqANpPrsJpGrEGJGNpYtvmD1wA99YzdEphWb

Merkle Root

80814aa8184372cdce8b1c2464b966f4a3cab80d0177dcf4fece8c53fc694156

Transactions (1)

Coinbase80814aa8184372…ce8c53fc694156

1 in → 43 out10.0800 XPM1.49 KB

ANpPrsJp…YzdEphWb ANWcCA1W…FYxSHbqJ AXDu24HR…L9o8sC5D ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

1.730 × 10⁸⁸(89-digit number)

17308900717653280282…30223135454663543399

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

1.730 × 10⁸⁸(89-digit number)

17308900717653280282…30223135454663543399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.461 × 10⁸⁸(89-digit number)

34617801435306560565…60446270909327086799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.923 × 10⁸⁸(89-digit number)

69235602870613121131…20892541818654173599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.384 × 10⁸⁹(90-digit number)

13847120574122624226…41785083637308347199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.769 × 10⁸⁹(90-digit number)

27694241148245248452…83570167274616694399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.538 × 10⁸⁹(90-digit number)

55388482296490496905…67140334549233388799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.107 × 10⁹⁰(91-digit number)

11077696459298099381…34280669098466777599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.215 × 10⁹⁰(91-digit number)

22155392918596198762…68561338196933555199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.431 × 10⁹⁰(91-digit number)

44310785837192397524…37122676393867110399

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