Block #286,508

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/30/2013, 10:29:18 PM · Difficulty 9.9856 · 6,518,758 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

56b160893ced0e7306b2ab82a53195729d85b258dc20a70e01687f8f4793d1ca

View on Chainz ↗

Height

#286,508

Difficulty

9.985644

Transactions

Size

720 B

Version

Bits

09fc5326

Nonce

23,961

Timestamp

11/30/2013, 10:29:18 PM

Confirmations

6,518,758

Mined by

⛏️ P2SHAVN5TcQu993EfviCkpQSYHiBxtuDJ9ZxKG

Merkle Root

8561c7d09aae5dd51202491001ae067fe6e1a349405b129b9d274e0dd5ffdf89

Transactions (2)

Coinbasec0701158e00764…3847dc23818464

1 in → 1 out10.0200 XPM110 B

AVN5TcQu…uDJ9ZxKG

e1bd3a7a881349…bb4fc80e56a516

3 in → 2 out41.4168 XPM522 B

AYaSXiFi…yqwqrHQZ APfVrodu…G36y94X4

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.

2.904 × 10⁹⁰(91-digit number)

29041039568385687755…80906415353631518719

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

2.904 × 10⁹⁰(91-digit number)

29041039568385687755…80906415353631518719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.808 × 10⁹⁰(91-digit number)

58082079136771375511…61812830707263037439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.161 × 10⁹¹(92-digit number)

11616415827354275102…23625661414526074879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.323 × 10⁹¹(92-digit number)

23232831654708550204…47251322829052149759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.646 × 10⁹¹(92-digit number)

46465663309417100409…94502645658104299519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.293 × 10⁹¹(92-digit number)

92931326618834200819…89005291316208599039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.858 × 10⁹²(93-digit number)

18586265323766840163…78010582632417198079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.717 × 10⁹²(93-digit number)

37172530647533680327…56021165264834396159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.434 × 10⁹²(93-digit number)

74345061295067360655…12042330529668792319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.486 × 10⁹³(94-digit number)

14869012259013472131…24084661059337584639

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