Block #340,421

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/2/2014, 6:39:50 PM · Difficulty 10.1329 · 6,465,660 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bbae492b895c6fabfcd975b6f7c7f442a82dc6cf1b470c73373c767ee93695a1

View on Chainz ↗

Height

#340,421

Difficulty

10.132939

Transactions

Size

972 B

Version

Bits

0a220850

Nonce

24,907

Timestamp

1/2/2014, 6:39:50 PM

Confirmations

6,465,660

Mined by

⛏️ 1aR4AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

aadbf15269e5d83ff19979581ace24bf04c0258fdb272953fea63dc3f4474a49

Transactions (1)

Coinbaseaadbf15269e5d8…a63dc3f4474a49

1 in → 24 out9.7189 XPM879 B

AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR AYtDvcGs…VuAcA7m7 AP5UvYhU…vLTDwkdA Ae58nAEb…GFUA15fv

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.

3.591 × 10¹⁰¹(102-digit number)

35912919111606598406…17326757064141646079

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

3.591 × 10¹⁰¹(102-digit number)

35912919111606598406…17326757064141646079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.182 × 10¹⁰¹(102-digit number)

71825838223213196813…34653514128283292159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.436 × 10¹⁰²(103-digit number)

14365167644642639362…69307028256566584319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.873 × 10¹⁰²(103-digit number)

28730335289285278725…38614056513133168639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.746 × 10¹⁰²(103-digit number)

57460670578570557451…77228113026266337279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.149 × 10¹⁰³(104-digit number)

11492134115714111490…54456226052532674559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.298 × 10¹⁰³(104-digit number)

22984268231428222980…08912452105065349119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.596 × 10¹⁰³(104-digit number)

45968536462856445960…17824904210130698239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.193 × 10¹⁰³(104-digit number)

91937072925712891921…35649808420261396479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.838 × 10¹⁰⁴(105-digit number)

18387414585142578384…71299616840522792959

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