Block #322,576

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/21/2013, 2:28:30 AM · Difficulty 10.1945 · 6,473,278 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

42acce04d92705b5a7cf02d9340a2dd59606869f69f56658383f563936204ef6

View on Chainz ↗

Height

#322,576

Difficulty

10.194458

Transactions

Size

1.05 KB

Version

Bits

0a31c7fa

Nonce

8,177

Timestamp

12/21/2013, 2:28:30 AM

Confirmations

6,473,278

Mined by

⛏️ aRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

4bc7bb085751c70cf22c0595985cf9d58e2e5e64a5c128b9d45a2b406ca34884

Transactions (1)

Coinbase4bc7bb085751c7…5a2b406ca34884

1 in → 27 out9.6100 XPM981 B

Ad9pSzHt…cpJ3y2zz AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AP5UvYhU…vLTDwkdA

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.

6.831 × 10¹⁰²(103-digit number)

68310043882671710169…38676945284347345119

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

6.831 × 10¹⁰²(103-digit number)

68310043882671710169…38676945284347345119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.366 × 10¹⁰³(104-digit number)

13662008776534342033…77353890568694690239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.732 × 10¹⁰³(104-digit number)

27324017553068684067…54707781137389380479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.464 × 10¹⁰³(104-digit number)

54648035106137368135…09415562274778760959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.092 × 10¹⁰⁴(105-digit number)

10929607021227473627…18831124549557521919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.185 × 10¹⁰⁴(105-digit number)

21859214042454947254…37662249099115043839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.371 × 10¹⁰⁴(105-digit number)

43718428084909894508…75324498198230087679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.743 × 10¹⁰⁴(105-digit number)

87436856169819789016…50648996396460175359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.748 × 10¹⁰⁵(106-digit number)

17487371233963957803…01297992792920350719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.497 × 10¹⁰⁵(106-digit number)

34974742467927915606…02595985585840701439

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