Block #385,686

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/1/2014, 11:17:04 PM · Difficulty 10.4055 · 6,408,751 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

96480d46c22774afe0d0889353e57bf5a1837c82a43836c990236b254d90b831

View on Chainz ↗

Height

#385,686

Difficulty

10.405464

Transactions

Size

1004 B

Version

Bits

0a67cc7a

Nonce

241,657

Timestamp

2/1/2014, 11:17:04 PM

Confirmations

6,408,751

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c6aa7df81f334dd6e48eca312699e1ba987988d1e0d62caf95e56e84173b881d

Transactions (2)

Coinbase1e3db942a1c929…57da8104017879

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

2057e5533989af…4f9f1979e613e8

4 in → 8 out21.8639 XPM804 B

AeKNrjNj…1NEq95Ta AJE7armk…BPD71XGi AKK3rNLb…fVc74Pom AN3sJRML…Lmqm3Bgx AJDkTayx…3p6w3pwS

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.

2.931 × 10⁹⁵(96-digit number)

29317164337657011683…46567647050206940159

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

2.931 × 10⁹⁵(96-digit number)

29317164337657011683…46567647050206940159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.863 × 10⁹⁵(96-digit number)

58634328675314023366…93135294100413880319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.172 × 10⁹⁶(97-digit number)

11726865735062804673…86270588200827760639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.345 × 10⁹⁶(97-digit number)

23453731470125609346…72541176401655521279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.690 × 10⁹⁶(97-digit number)

46907462940251218693…45082352803311042559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.381 × 10⁹⁶(97-digit number)

93814925880502437386…90164705606622085119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.876 × 10⁹⁷(98-digit number)

18762985176100487477…80329411213244170239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.752 × 10⁹⁷(98-digit number)

37525970352200974954…60658822426488340479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.505 × 10⁹⁷(98-digit number)

75051940704401949909…21317644852976680959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.501 × 10⁹⁸(99-digit number)

15010388140880389981…42635289705953361919

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