Block #339,471

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/2/2014, 3:29:02 AM · Difficulty 10.1258 · 6,455,962 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cd02e8da4d72260d66cc8fa2faa44b1559ab62856b7122d4847d16489867923a

View on Chainz ↗

Height

#339,471

Difficulty

10.125832

Transactions

Size

47.93 KB

Version

Bits

0a203686

Nonce

54,279

Timestamp

1/2/2014, 3:29:02 AM

Confirmations

6,455,962

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

451db7b0f6e0de266d3d3bab2159aa436f950752a8da34e0ff355e553067a14a

Transactions (2)

Coinbase618dc46e361661…b8b32fc4ad9f6f

1 in → 1 out10.2300 XPM110 B

AeKNrjNj…1NEq95Ta

873189dfa97f0a…90e4c6559165dd

330 in → 1 out345.0688 XPM47.73 KB

AJeSvLws…vZu3PLEP

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.

1.716 × 10⁹⁹(100-digit number)

17161627026721533874…46335327838677652479

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

1.716 × 10⁹⁹(100-digit number)

17161627026721533874…46335327838677652479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.432 × 10⁹⁹(100-digit number)

34323254053443067748…92670655677355304959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.864 × 10⁹⁹(100-digit number)

68646508106886135497…85341311354710609919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.372 × 10¹⁰⁰(101-digit number)

13729301621377227099…70682622709421219839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.745 × 10¹⁰⁰(101-digit number)

27458603242754454199…41365245418842439679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.491 × 10¹⁰⁰(101-digit number)

54917206485508908398…82730490837684879359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.098 × 10¹⁰¹(102-digit number)

10983441297101781679…65460981675369758719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.196 × 10¹⁰¹(102-digit number)

21966882594203563359…30921963350739517439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.393 × 10¹⁰¹(102-digit number)

43933765188407126718…61843926701479034879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.786 × 10¹⁰¹(102-digit number)

87867530376814253436…23687853402958069759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

1.757 × 10¹⁰²(103-digit number)

17573506075362850687…47375706805916139519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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