Block #244,202

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/4/2013, 5:32:54 PM · Difficulty 9.9627 · 6,552,316 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5ecda5b53243f255137433252e1dc1197ec341d3b4a944a48203d0b8d64099be

View on Chainz ↗

Height

#244,202

Difficulty

9.962662

Transactions

Size

1.77 KB

Version

Bits

09f670fe

Nonce

22,166

Timestamp

11/4/2013, 5:32:54 PM

Confirmations

6,552,316

Mined by

⛏️ RwWAeZmMFY8rB8UkmiuS99wvBUeE9mjAy5Mi4

Merkle Root

c79a68f39b3a072a86fe25c077cf37437e924b5446d7427d5a2b55bf31e78046

Transactions (1)

Coinbasec79a68f39b3a07…2b55bf31e78046

1 in → 49 out10.0400 XPM1.69 KB

AeZmMFY8…mjAy5Mi4 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AZWiC56x…NwextJca AU9KdB9r…o5XC6WMy

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.

2.200 × 10⁸⁹(90-digit number)

22002103054240691432…19222277355049062079

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

2.200 × 10⁸⁹(90-digit number)

22002103054240691432…19222277355049062079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.400 × 10⁸⁹(90-digit number)

44004206108481382865…38444554710098124159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.800 × 10⁸⁹(90-digit number)

88008412216962765731…76889109420196248319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.760 × 10⁹⁰(91-digit number)

17601682443392553146…53778218840392496639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.520 × 10⁹⁰(91-digit number)

35203364886785106292…07556437680784993279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.040 × 10⁹⁰(91-digit number)

70406729773570212584…15112875361569986559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.408 × 10⁹¹(92-digit number)

14081345954714042516…30225750723139973119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.816 × 10⁹¹(92-digit number)

28162691909428085033…60451501446279946239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.632 × 10⁹¹(92-digit number)

56325383818856170067…20903002892559892479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.126 × 10⁹²(93-digit number)

11265076763771234013…41806005785119784959

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