Block #473,435

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/3/2014, 9:43:36 PM · Difficulty 10.4476 · 6,330,381 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

609552c6d525c5a3d3c83eff4d0cca32232388083b9481addcc9005c6741cd85

View on Chainz ↗

Height

#473,435

Difficulty

10.447610

Transactions

Size

936 B

Version

Bits

0a729698

Nonce

167,256

Timestamp

4/3/2014, 9:43:36 PM

Confirmations

6,330,381

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

e5680a099c27bc10905b684dd5f2e5028b04b5aa64fca759c03da66ee09120bf

Transactions (1)

Coinbasee5680a099c27bc…3da66ee09120bf

1 in → 23 out9.1500 XPM845 B

AdFLJFhb…bsaVkAyh AdoqUYAy…tJ482T9b AUFKXvnz…342ApNcm AUzEPJFG…kYkA5U9V ASgUri65…C7NLcyBg

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.

1.034 × 10⁹⁷(98-digit number)

10341144114154119011…10098189311150745599

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

1.034 × 10⁹⁷(98-digit number)

10341144114154119011…10098189311150745599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.068 × 10⁹⁷(98-digit number)

20682288228308238023…20196378622301491199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.136 × 10⁹⁷(98-digit number)

41364576456616476046…40392757244602982399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.272 × 10⁹⁷(98-digit number)

82729152913232952092…80785514489205964799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.654 × 10⁹⁸(99-digit number)

16545830582646590418…61571028978411929599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.309 × 10⁹⁸(99-digit number)

33091661165293180836…23142057956823859199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.618 × 10⁹⁸(99-digit number)

66183322330586361673…46284115913647718399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.323 × 10⁹⁹(100-digit number)

13236664466117272334…92568231827295436799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.647 × 10⁹⁹(100-digit number)

26473328932234544669…85136463654590873599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.294 × 10⁹⁹(100-digit number)

52946657864469089339…70272927309181747199

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