Block #394,542

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/8/2014, 1:01:47 AM · Difficulty 10.4215 · 6,415,876 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d9799aa6802183a607d57fd2469a1f3672b2514a0fd2a1faddee729344e30f0a

View on Chainz ↗

Height

#394,542

Difficulty

10.421498

Transactions

Size

202 B

Version

Bits

0a6be753

Nonce

505,811

Timestamp

2/8/2014, 1:01:47 AM

Confirmations

6,415,876

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f797ee8d2a319c4f24c4fe394d19fe9cf43bed62adb2c0f5b2482ea8540c1da2

Transactions (1)

Coinbasef797ee8d2a319c…482ea8540c1da2

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

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.

9.700 × 10⁹⁹(100-digit number)

97009562975423835104…62791764592602150399

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

9.700 × 10⁹⁹(100-digit number)

97009562975423835104…62791764592602150399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.940 × 10¹⁰⁰(101-digit number)

19401912595084767020…25583529185204300799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.880 × 10¹⁰⁰(101-digit number)

38803825190169534041…51167058370408601599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.760 × 10¹⁰⁰(101-digit number)

77607650380339068083…02334116740817203199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.552 × 10¹⁰¹(102-digit number)

15521530076067813616…04668233481634406399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.104 × 10¹⁰¹(102-digit number)

31043060152135627233…09336466963268812799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.208 × 10¹⁰¹(102-digit number)

62086120304271254466…18672933926537625599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.241 × 10¹⁰²(103-digit number)

12417224060854250893…37345867853075251199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.483 × 10¹⁰²(103-digit number)

24834448121708501786…74691735706150502399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.966 × 10¹⁰²(103-digit number)

49668896243417003573…49383471412301004799

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

Block #394,542

Cookie Preferences