Block #462,908

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/27/2014, 6:01:15 PM · Difficulty 10.4169 · 6,335,228 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d4aee1823a9d371cb57ee1ecbec4a4f48f7d6aa6a856aa7e8929fa4cbc230aa2

View on Chainz ↗

Height

#462,908

Difficulty

10.416903

Transactions

Size

208 B

Version

Bits

0a6aba2a

Nonce

4,045

Timestamp

3/27/2014, 6:01:15 PM

Confirmations

6,335,228

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

4cebd11279233456fcefc270e3279bbaf7148f418f10764c62ac33006effcf15

Transactions (1)

Coinbase4cebd112792334…ac33006effcf15

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

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.

8.629 × 10⁹⁹(100-digit number)

86294892491978779833…61763566499957122599

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

8.629 × 10⁹⁹(100-digit number)

86294892491978779833…61763566499957122599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.725 × 10¹⁰⁰(101-digit number)

17258978498395755966…23527132999914245199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.451 × 10¹⁰⁰(101-digit number)

34517956996791511933…47054265999828490399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.903 × 10¹⁰⁰(101-digit number)

69035913993583023866…94108531999656980799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.380 × 10¹⁰¹(102-digit number)

13807182798716604773…88217063999313961599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.761 × 10¹⁰¹(102-digit number)

27614365597433209546…76434127998627923199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.522 × 10¹⁰¹(102-digit number)

55228731194866419093…52868255997255846399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.104 × 10¹⁰²(103-digit number)

11045746238973283818…05736511994511692799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.209 × 10¹⁰²(103-digit number)

22091492477946567637…11473023989023385599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.418 × 10¹⁰²(103-digit number)

44182984955893135274…22946047978046771199

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