Block #430,340

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/5/2014, 10:49:28 AM · Difficulty 10.3413 · 6,372,165 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bd4daf21f7e15808d106bb7fac39b034efee6b937a0f85113360655f62b87a48

View on Chainz ↗

Height

#430,340

Difficulty

10.341282

Transactions

Size

384 B

Version

Bits

0a575e43

Nonce

608,988

Timestamp

3/5/2014, 10:49:28 AM

Confirmations

6,372,165

Mined by

⛏️ P2SHASXb8Msj7tnyLvWQxYzaaZ1YewBxGf64iZ

Merkle Root

7937a43d7b7fec2df37954c52f074d02f9dabc1c67614a0f7c2f474f3434944a

Transactions (2)

Coinbase4a3a933877ef33…b690745b8b0a3a

1 in → 1 out9.3519 XPM101 B

ASXb8Msj…BxGf64iZ

6b56d3ef2a6373…328c42a24dacac

1 in → 1 out0.9900 XPM191 B

ARxpQYdD…q9Bde3dv

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.

3.108 × 10⁹⁹(100-digit number)

31089605645341507821…91877723156215818239

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

3.108 × 10⁹⁹(100-digit number)

31089605645341507821…91877723156215818239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.217 × 10⁹⁹(100-digit number)

62179211290683015643…83755446312431636479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.243 × 10¹⁰⁰(101-digit number)

12435842258136603128…67510892624863272959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.487 × 10¹⁰⁰(101-digit number)

24871684516273206257…35021785249726545919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.974 × 10¹⁰⁰(101-digit number)

49743369032546412514…70043570499453091839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.948 × 10¹⁰⁰(101-digit number)

99486738065092825029…40087140998906183679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.989 × 10¹⁰¹(102-digit number)

19897347613018565005…80174281997812367359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.979 × 10¹⁰¹(102-digit number)

39794695226037130011…60348563995624734719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.958 × 10¹⁰¹(102-digit number)

79589390452074260023…20697127991249469439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.591 × 10¹⁰²(103-digit number)

15917878090414852004…41394255982498938879

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