Block #400,248

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/11/2014, 10:50:40 PM · Difficulty 10.4325 · 6,405,451 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

619b7c58906146cd645e4c77e07753b51657ceedfb6ca8206f807a2c3b780ac7

View on Chainz ↗

Height

#400,248

Difficulty

10.432452

Transactions

Size

3.28 KB

Version

Bits

0a6eb52d

Nonce

106,776

Timestamp

2/11/2014, 10:50:40 PM

Confirmations

6,405,451

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

159fb448da7bc57a4350177a485f556e28b3bbbcf5c71d82ce7e5dc4eb430038

Transactions (2)

Coinbase3402a10f7c8da1…4cbf5381427401

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

19eadd7577b4e6…23af145be0e649

21 in → 1 out64.2484 XPM3.07 KB

Aa9TdDYz…3oKRZ7Es

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.

9.289 × 10⁹⁸(99-digit number)

92899272144206967114…06952750914912689599

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

9.289 × 10⁹⁸(99-digit number)

92899272144206967114…06952750914912689599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.857 × 10⁹⁹(100-digit number)

18579854428841393422…13905501829825379199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.715 × 10⁹⁹(100-digit number)

37159708857682786845…27811003659650758399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.431 × 10⁹⁹(100-digit number)

74319417715365573691…55622007319301516799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.486 × 10¹⁰⁰(101-digit number)

14863883543073114738…11244014638603033599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.972 × 10¹⁰⁰(101-digit number)

29727767086146229476…22488029277206067199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.945 × 10¹⁰⁰(101-digit number)

59455534172292458953…44976058554412134399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.189 × 10¹⁰¹(102-digit number)

11891106834458491790…89952117108824268799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.378 × 10¹⁰¹(102-digit number)

23782213668916983581…79904234217648537599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.756 × 10¹⁰¹(102-digit number)

47564427337833967162…59808468435297075199

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