Block #301,043

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/8/2013, 10:45:17 PM · Difficulty 9.9925 · 6,505,185 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

395cb68c6629d4523a52336a033a1657d2d7b954e35281ac414ba488253405ee

View on Chainz ↗

Height

#301,043

Difficulty

9.992478

Transactions

Size

1.11 KB

Version

Bits

09fe1304

Nonce

1,802

Timestamp

12/8/2013, 10:45:17 PM

Confirmations

6,505,185

Mined by

⛏️ aR~3AYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

b223eb78678cdbd57dc1a9d709244feeb1e81dbca8276c8bc4a80128ffd18d99

Transactions (1)

Coinbaseb223eb78678cdb…a80128ffd18d99

1 in → 29 out9.9800 XPM1.02 KB

AYtDvcGs…VuAcA7m7 AYcLTeXR…bscgPops Ad9pSzHt…cpJ3y2zz AQwRN8bE…V8PsTcY9 AZ2pPuKg…95SN2Yr7

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.

5.703 × 10⁹⁷(98-digit number)

57038009693851265949…01266615744607774719

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

5.703 × 10⁹⁷(98-digit number)

57038009693851265949…01266615744607774719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.140 × 10⁹⁸(99-digit number)

11407601938770253189…02533231489215549439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.281 × 10⁹⁸(99-digit number)

22815203877540506379…05066462978431098879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.563 × 10⁹⁸(99-digit number)

45630407755081012759…10132925956862197759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.126 × 10⁹⁸(99-digit number)

91260815510162025519…20265851913724395519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.825 × 10⁹⁹(100-digit number)

18252163102032405103…40531703827448791039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.650 × 10⁹⁹(100-digit number)

36504326204064810207…81063407654897582079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.300 × 10⁹⁹(100-digit number)

73008652408129620415…62126815309795164159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.460 × 10¹⁰⁰(101-digit number)

14601730481625924083…24253630619590328319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.920 × 10¹⁰⁰(101-digit number)

29203460963251848166…48507261239180656639

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