Block #424,169

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/1/2014, 12:23:00 AM · Difficulty 10.3655 · 6,373,674 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f5117e9177d2997b7f005d8184221e67588be7d1e517ffeba37177e6d7bcea91

View on Chainz ↗

Height

#424,169

Difficulty

10.365550

Transactions

Size

394 B

Version

Bits

0a5d94aa

Nonce

35,208

Timestamp

3/1/2014, 12:23:00 AM

Confirmations

6,373,674

Mined by

⛏️ P2SHAXvrwWvTs4z9NGHKpy1dk5FTfjxtUE9tjk

Merkle Root

74cd4520109ba6dda999f8bb91d2b7a9ca0fd6b0979dd940a033ef43a651241f

Transactions (2)

Coinbase4448cf35a3c908…be30d0cffe6238

1 in → 1 out9.3000 XPM109 B

AXvrwWvT…xtUE9tjk

2674aabb993ba7…d58ea07249b4fa

1 in → 1 out3.1059 XPM193 B

AFwD4q46…sxTWDQig

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.

7.960 × 10⁹⁸(99-digit number)

79605615134594806895…76763673664011555239

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

7.960 × 10⁹⁸(99-digit number)

79605615134594806895…76763673664011555239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.592 × 10⁹⁹(100-digit number)

15921123026918961379…53527347328023110479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.184 × 10⁹⁹(100-digit number)

31842246053837922758…07054694656046220959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.368 × 10⁹⁹(100-digit number)

63684492107675845516…14109389312092441919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.273 × 10¹⁰⁰(101-digit number)

12736898421535169103…28218778624184883839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.547 × 10¹⁰⁰(101-digit number)

25473796843070338206…56437557248369767679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.094 × 10¹⁰⁰(101-digit number)

50947593686140676413…12875114496739535359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.018 × 10¹⁰¹(102-digit number)

10189518737228135282…25750228993479070719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.037 × 10¹⁰¹(102-digit number)

20379037474456270565…51500457986958141439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.075 × 10¹⁰¹(102-digit number)

40758074948912541130…03000915973916282879

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