Block #580,514

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/7/2014, 8:45:02 PM · Difficulty 10.9649 · 6,214,873 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

906efccb2370d5bc413a8d4e558df68ddd2d1673eaab5a85ef1fe9e218393328

View on Chainz ↗

Height

#580,514

Difficulty

10.964875

Transactions

Size

244 B

Version

Bits

0af70206

Nonce

2,370,763

Timestamp

6/7/2014, 8:45:02 PM

Confirmations

6,214,873

Mined by

⛏️ P2SHAXn1KW6PTFKBcGVcbZ8CPoUc4Pc7VDu2zv

Merkle Root

342b57080fd04e38983e60fcf4b2eb92281069110b5e0c1aef060c5da82ab3c8

Transactions (1)

Coinbase342b57080fd04e…060c5da82ab3c8

1 in → 2 out8.3000 XPM152 B

AXn1KW6P…c7VDu2zv ALPu3s2c…EJXLjVFh

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.

6.843 × 10⁹⁹(100-digit number)

68437134435877297428…57757799856659312639

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

6.843 × 10⁹⁹(100-digit number)

68437134435877297428…57757799856659312639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.368 × 10¹⁰⁰(101-digit number)

13687426887175459485…15515599713318625279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.737 × 10¹⁰⁰(101-digit number)

27374853774350918971…31031199426637250559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.474 × 10¹⁰⁰(101-digit number)

54749707548701837942…62062398853274501119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.094 × 10¹⁰¹(102-digit number)

10949941509740367588…24124797706549002239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.189 × 10¹⁰¹(102-digit number)

21899883019480735177…48249595413098004479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.379 × 10¹⁰¹(102-digit number)

43799766038961470354…96499190826196008959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.759 × 10¹⁰¹(102-digit number)

87599532077922940708…92998381652392017919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.751 × 10¹⁰²(103-digit number)

17519906415584588141…85996763304784035839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.503 × 10¹⁰²(103-digit number)

35039812831169176283…71993526609568071679

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