Block #431,226

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/6/2014, 1:56:26 AM · Difficulty 10.3388 · 6,364,110 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

673fd9f42680c4ee72e1b69970434e7caaa43faecbf849e54860579d01965816

View on Chainz ↗

Height

#431,226

Difficulty

10.338829

Transactions

Size

1.05 KB

Version

Bits

0a56bd80

Nonce

44,236

Timestamp

3/6/2014, 1:56:26 AM

Confirmations

6,364,110

Mined by

⛏️ zaSAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

cc9cb1aadfe57cb714b5255a9bb43f1c394fe9d9bef9b96813b3cac797077963

Transactions (1)

Coinbasecc9cb1aadfe57c…b3cac797077963

1 in → 27 out9.3400 XPM981 B

Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AFutDVqJ…TJTJj6UF

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.

2.583 × 10⁹⁹(100-digit number)

25836373871315121209…47486342799435196799

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

2.583 × 10⁹⁹(100-digit number)

25836373871315121209…47486342799435196799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.167 × 10⁹⁹(100-digit number)

51672747742630242418…94972685598870393599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.033 × 10¹⁰⁰(101-digit number)

10334549548526048483…89945371197740787199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.066 × 10¹⁰⁰(101-digit number)

20669099097052096967…79890742395481574399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.133 × 10¹⁰⁰(101-digit number)

41338198194104193934…59781484790963148799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.267 × 10¹⁰⁰(101-digit number)

82676396388208387869…19562969581926297599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.653 × 10¹⁰¹(102-digit number)

16535279277641677573…39125939163852595199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.307 × 10¹⁰¹(102-digit number)

33070558555283355147…78251878327705190399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.614 × 10¹⁰¹(102-digit number)

66141117110566710295…56503756655410380799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.322 × 10¹⁰²(103-digit number)

13228223422113342059…13007513310820761599

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