Block #247,289

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/6/2013, 4:16:26 PM · Difficulty 9.9649 · 6,555,197 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7aa27073bead75e1ab4e312324d8ce2c922dab95875980960c7b5ef32c1374eb

View on Chainz ↗

Height

#247,289

Difficulty

9.964854

Transactions

Size

2.11 KB

Version

Bits

09f700a4

Nonce

38,814

Timestamp

11/6/2013, 4:16:26 PM

Confirmations

6,555,197

Mined by

⛏️ RzkPANo4YY1xjeppLPNm9kAdtJjYCnvnsPRDSU

Merkle Root

462ab2da720e7aa1b27f90a53757aebc305615a160b0865ddf858d15e5779961

Transactions (1)

Coinbase462ab2da720e7a…858d15e5779961

1 in → 59 out10.0299 XPM2.02 KB

ANo4YY1x…vnsPRDSU ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk Aaf3CsqS…k1Eu3vmJ 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.

5.767 × 10⁹²(93-digit number)

57671134414033483615…79307719308228724719

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

5.767 × 10⁹²(93-digit number)

57671134414033483615…79307719308228724719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.153 × 10⁹³(94-digit number)

11534226882806696723…58615438616457449439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.306 × 10⁹³(94-digit number)

23068453765613393446…17230877232914898879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.613 × 10⁹³(94-digit number)

46136907531226786892…34461754465829797759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.227 × 10⁹³(94-digit number)

92273815062453573784…68923508931659595519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.845 × 10⁹⁴(95-digit number)

18454763012490714756…37847017863319191039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.690 × 10⁹⁴(95-digit number)

36909526024981429513…75694035726638382079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.381 × 10⁹⁴(95-digit number)

73819052049962859027…51388071453276764159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.476 × 10⁹⁵(96-digit number)

14763810409992571805…02776142906553528319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.952 × 10⁹⁵(96-digit number)

29527620819985143611…05552285813107056639

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer