Block #506,630

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/23/2014, 5:29:15 AM · Difficulty 10.8140 · 6,304,236 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e767e3ffc60302191961b50811d2a7aee80bf4cc1ab24b00e94a2eb714fd4248

View on Chainz ↗

Height

#506,630

Difficulty

10.813990

Transactions

Size

797 B

Version

Bits

0ad061a3

Nonce

62,305

Timestamp

4/23/2014, 5:29:15 AM

Confirmations

6,304,236

Mined by

AREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

1b2f5cb241ad08fd37ae52331b5067bb0eef2acdae09123763a6088c37ff4fcd

Transactions (1)

Coinbase1b2f5cb241ad08…a6088c37ff4fcd

1 in → 19 out8.5400 XPM709 B

AREQGaCC…V47D9Shh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AXCpMYgL…1r94ZQDa AbPcCMg4…719q6mAX

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.

2.285 × 10⁸⁹(90-digit number)

22857721372768364520…59551448673576963201

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

2.285 × 10⁸⁹(90-digit number)

22857721372768364520…59551448673576963201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.571 × 10⁸⁹(90-digit number)

45715442745536729040…19102897347153926401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.143 × 10⁸⁹(90-digit number)

91430885491073458080…38205794694307852801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.828 × 10⁹⁰(91-digit number)

18286177098214691616…76411589388615705601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.657 × 10⁹⁰(91-digit number)

36572354196429383232…52823178777231411201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.314 × 10⁹⁰(91-digit number)

73144708392858766464…05646357554462822401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.462 × 10⁹¹(92-digit number)

14628941678571753292…11292715108925644801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.925 × 10⁹¹(92-digit number)

29257883357143506585…22585430217851289601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.851 × 10⁹¹(92-digit number)

58515766714287013171…45170860435702579201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.170 × 10⁹²(93-digit number)

11703153342857402634…90341720871405158401

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #506,630

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