Block #510,486

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/25/2014, 4:34:32 PM · Difficulty 10.8252 · 6,295,312 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f1ef8106f0fed8b0c23cf8e7fb995022ca4c2440f99f89fe17f04b2457ee0807

View on Chainz ↗

Height

#510,486

Difficulty

10.825173

Transactions

Size

208 B

Version

Bits

0ad33e8e

Nonce

254,495,430

Timestamp

4/25/2014, 4:34:32 PM

Confirmations

6,295,312

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5ad62386d571efacf6541f26d65907ff46327582a5fed0614dc5a23ec4794a2b

Transactions (1)

Coinbase5ad62386d571ef…c5a23ec4794a2b

1 in → 1 out8.5200 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.

2.508 × 10⁹⁹(100-digit number)

25084061026091511383…29072934128734189759

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

2.508 × 10⁹⁹(100-digit number)

25084061026091511383…29072934128734189759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.016 × 10⁹⁹(100-digit number)

50168122052183022766…58145868257468379519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.003 × 10¹⁰⁰(101-digit number)

10033624410436604553…16291736514936759039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.006 × 10¹⁰⁰(101-digit number)

20067248820873209106…32583473029873518079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.013 × 10¹⁰⁰(101-digit number)

40134497641746418213…65166946059747036159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.026 × 10¹⁰⁰(101-digit number)

80268995283492836426…30333892119494072319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.605 × 10¹⁰¹(102-digit number)

16053799056698567285…60667784238988144639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.210 × 10¹⁰¹(102-digit number)

32107598113397134570…21335568477976289279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.421 × 10¹⁰¹(102-digit number)

64215196226794269141…42671136955952578559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.284 × 10¹⁰²(103-digit number)

12843039245358853828…85342273911905157119

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