Block #246,915

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/6/2013, 11:04:35 AM · Difficulty 9.9644 · 6,562,983 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

3c12db53498bce66a3dfeedf8c0e8d9faa6df337945069f3632bb42aa5fada49

View on Chainz ↗

Height

#246,915

Difficulty

9.964382

Transactions

Size

1.84 KB

Version

Bits

09f6e1c3

Nonce

8,180

Timestamp

11/6/2013, 11:04:35 AM

Confirmations

6,562,983

Mined by

⛏️ Rz"ANkcZeE6iiYJEXGGojdDWzmqBWbVux83Yj

Merkle Root

643c0fc91592ec1d3244f6a82bdbb33cf1cb19703e2a911940df7125bbe43b49

Transactions (1)

Coinbase643c0fc91592ec…df7125bbe43b49

1 in → 51 out10.0400 XPM1.75 KB

ANkcZeE6…bVux83Yj ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AT3ATVPt…Qw6x41k1 AJNMkswR…SnXAFUHL

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.

6.784 × 10⁹⁸(99-digit number)

67844604846198072957…40265289396054149999

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

6.784 × 10⁹⁸(99-digit number)

67844604846198072957…40265289396054149999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.356 × 10⁹⁹(100-digit number)

13568920969239614591…80530578792108299999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.713 × 10⁹⁹(100-digit number)

27137841938479229183…61061157584216599999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.427 × 10⁹⁹(100-digit number)

54275683876958458366…22122315168433199999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.085 × 10¹⁰⁰(101-digit number)

10855136775391691673…44244630336866399999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.171 × 10¹⁰⁰(101-digit number)

21710273550783383346…88489260673732799999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.342 × 10¹⁰⁰(101-digit number)

43420547101566766692…76978521347465599999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.684 × 10¹⁰⁰(101-digit number)

86841094203133533385…53957042694931199999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.736 × 10¹⁰¹(102-digit number)

17368218840626706677…07914085389862399999

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 #246,915

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