Block #494,686

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/16/2014, 7:01:47 AM · Difficulty 10.7236 · 6,318,316 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0b676eb8e396df64fea47ea759201fceeb728020fd0e4b11a25100b1f59070d6

View on Chainz ↗

Height

#494,686

Difficulty

10.723559

Transactions

Size

208 B

Version

Bits

0ab93b2e

Nonce

355,154

Timestamp

4/16/2014, 7:01:47 AM

Confirmations

6,318,316

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

26f00f618e0c08c11f8922cbd70ee93bd144e6546de3c7577a3112fdc7416c05

Transactions (1)

Coinbase26f00f618e0c08…3112fdc7416c05

1 in → 1 out8.6800 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.

1.356 × 10⁹⁹(100-digit number)

13560277659854905024…00068169221171822199

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

1.356 × 10⁹⁹(100-digit number)

13560277659854905024…00068169221171822199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.712 × 10⁹⁹(100-digit number)

27120555319709810049…00136338442343644399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.424 × 10⁹⁹(100-digit number)

54241110639419620099…00272676884687288799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.084 × 10¹⁰⁰(101-digit number)

10848222127883924019…00545353769374577599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.169 × 10¹⁰⁰(101-digit number)

21696444255767848039…01090707538749155199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.339 × 10¹⁰⁰(101-digit number)

43392888511535696079…02181415077498310399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.678 × 10¹⁰⁰(101-digit number)

86785777023071392158…04362830154996620799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.735 × 10¹⁰¹(102-digit number)

17357155404614278431…08725660309993241599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.471 × 10¹⁰¹(102-digit number)

34714310809228556863…17451320619986483199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.942 × 10¹⁰¹(102-digit number)

69428621618457113727…34902641239972966399

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

Block #494,686

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