Block #432,531

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/6/2014, 11:26:51 PM · Difficulty 10.3412 · 6,376,847 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e1e4e4aa7632db7cda4bf55bad6252ac3866c83b8f004d110abfe65e44d03d02

View on Chainz ↗

Height

#432,531

Difficulty

10.341171

Transactions

Size

1003 B

Version

Bits

0a5756fc

Nonce

52,376

Timestamp

3/6/2014, 11:26:51 PM

Confirmations

6,376,847

Mined by

⛏️ aSZAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

50e268cd7d723e7a781862f309685920bc913ac7cbfa8f4ecec36d105aaf638f

Transactions (1)

Coinbase50e268cd7d723e…c36d105aaf638f

1 in → 25 out9.3400 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

4.013 × 10⁹⁵(96-digit number)

40137126549294966008…13106605307717802639

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

4.013 × 10⁹⁵(96-digit number)

40137126549294966008…13106605307717802639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.027 × 10⁹⁵(96-digit number)

80274253098589932016…26213210615435605279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.605 × 10⁹⁶(97-digit number)

16054850619717986403…52426421230871210559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.210 × 10⁹⁶(97-digit number)

32109701239435972806…04852842461742421119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.421 × 10⁹⁶(97-digit number)

64219402478871945613…09705684923484842239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.284 × 10⁹⁷(98-digit number)

12843880495774389122…19411369846969684479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.568 × 10⁹⁷(98-digit number)

25687760991548778245…38822739693939368959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.137 × 10⁹⁷(98-digit number)

51375521983097556490…77645479387878737919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.027 × 10⁹⁸(99-digit number)

10275104396619511298…55290958775757475839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.055 × 10⁹⁸(99-digit number)

20550208793239022596…10581917551514951679

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 #432,531

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