Block #510,274

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/25/2014, 1:38:40 PM · Difficulty 10.8239 · 6,280,671 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1e3248d776b2b42ed4949bf0b4ad832937c4a9aa1118fffb373a71aa3c4d2754

View on Chainz ↗

Height

#510,274

Difficulty

10.823901

Transactions

Size

203 B

Version

Bits

0ad2eb2c

Nonce

35,335

Timestamp

4/25/2014, 1:38:40 PM

Confirmations

6,280,671

Merkle Root

2dd0f7f15d69fb3bd8ffb6888bd1277a1cf7e58b5a658203bae26267311bd156

Transactions (1)

Coinbase2dd0f7f15d69fb…e26267311bd156

1 in → 1 out8.5200 XPM109 B

AdR3SMVt…2zrhAR7g

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.

2.238 × 10¹⁰⁵(106-digit number)

22382258867432655945…21832289651323580159

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

2.238 × 10¹⁰⁵(106-digit number)

22382258867432655945…21832289651323580159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.476 × 10¹⁰⁵(106-digit number)

44764517734865311891…43664579302647160319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.952 × 10¹⁰⁵(106-digit number)

89529035469730623783…87329158605294320639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.790 × 10¹⁰⁶(107-digit number)

17905807093946124756…74658317210588641279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.581 × 10¹⁰⁶(107-digit number)

35811614187892249513…49316634421177282559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.162 × 10¹⁰⁶(107-digit number)

71623228375784499027…98633268842354565119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.432 × 10¹⁰⁷(108-digit number)

14324645675156899805…97266537684709130239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.864 × 10¹⁰⁷(108-digit number)

28649291350313799610…94533075369418260479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.729 × 10¹⁰⁷(108-digit number)

57298582700627599221…89066150738836520959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.145 × 10¹⁰⁸(109-digit number)

11459716540125519844…78132301477673041919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.291 × 10¹⁰⁸(109-digit number)

22919433080251039688…56264602955346083839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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