Block #470,682

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/2/2014, 2:18:42 AM · Difficulty 10.4297 · 6,326,135 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e3d8782329d8428372c2044b41e2c1c93aebb668b2e60d7d5370b2b2536ed96e

View on Chainz ↗

Height

#470,682

Difficulty

10.429691

Transactions

Size

971 B

Version

Bits

0a6e0035

Nonce

62,265

Timestamp

4/2/2014, 2:18:42 AM

Confirmations

6,326,135

Mined by

⛏️ .iAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

c876490619c7aa5642ebabf9edfb4c6251e6ad47ea80f57bb233671dc4a39482

Transactions (1)

Coinbasec876490619c7aa…33671dc4a39482

1 in → 24 out9.1800 XPM879 B

AdFLJFhb…bsaVkAyh ASgUri65…C7NLcyBg AUFKXvnz…342ApNcm Adbb4svj…dQWTHsq5 AGz9gyZW…bo8NYQpw

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.

8.646 × 10⁹⁸(99-digit number)

86466612047133338803…83510069917765038079

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

8.646 × 10⁹⁸(99-digit number)

86466612047133338803…83510069917765038079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.729 × 10⁹⁹(100-digit number)

17293322409426667760…67020139835530076159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.458 × 10⁹⁹(100-digit number)

34586644818853335521…34040279671060152319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.917 × 10⁹⁹(100-digit number)

69173289637706671043…68080559342120304639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.383 × 10¹⁰⁰(101-digit number)

13834657927541334208…36161118684240609279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.766 × 10¹⁰⁰(101-digit number)

27669315855082668417…72322237368481218559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.533 × 10¹⁰⁰(101-digit number)

55338631710165336834…44644474736962437119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.106 × 10¹⁰¹(102-digit number)

11067726342033067366…89288949473924874239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.213 × 10¹⁰¹(102-digit number)

22135452684066134733…78577898947849748479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.427 × 10¹⁰¹(102-digit number)

44270905368132269467…57155797895699496959

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