Block #430,273

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/5/2014, 9:40:25 AM · Difficulty 10.3416 · 6,376,492 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e92eae4a8a4524004ed033eb42faf23870801f940095ad5740cde72ff78a04cd

View on Chainz ↗

Height

#430,273

Difficulty

10.341579

Transactions

Size

1003 B

Version

Bits

0a5771b2

Nonce

158,438

Timestamp

3/5/2014, 9:40:25 AM

Confirmations

6,376,492

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e3d36f5ff8ed3db5c60a6c2ba8945eb730cc5fd5155846cde3d50443e3275800

Transactions (1)

Coinbasee3d36f5ff8ed3d…d50443e3275800

1 in → 25 out9.3400 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

9.489 × 10⁹⁴(95-digit number)

94895576897260167171…18641692081544900799

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

9.489 × 10⁹⁴(95-digit number)

94895576897260167171…18641692081544900799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.897 × 10⁹⁵(96-digit number)

18979115379452033434…37283384163089801599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.795 × 10⁹⁵(96-digit number)

37958230758904066868…74566768326179603199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.591 × 10⁹⁵(96-digit number)

75916461517808133737…49133536652359206399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.518 × 10⁹⁶(97-digit number)

15183292303561626747…98267073304718412799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.036 × 10⁹⁶(97-digit number)

30366584607123253494…96534146609436825599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.073 × 10⁹⁶(97-digit number)

60733169214246506989…93068293218873651199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.214 × 10⁹⁷(98-digit number)

12146633842849301397…86136586437747302399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.429 × 10⁹⁷(98-digit number)

24293267685698602795…72273172875494604799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.858 × 10⁹⁷(98-digit number)

48586535371397205591…44546345750989209599

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

Block #430,273

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