Block #277,918

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 6:43:06 PM · Difficulty 9.9676 · 6,513,608 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

456513aa7b4136f979056f2fdb643568208e598d0a16fa127517c339b2b96ab6

View on Chainz ↗

Height

#277,918

Difficulty

9.967553

Transactions

Size

1.15 KB

Version

Bits

09f7b18f

Nonce

17,676

Timestamp

11/27/2013, 6:43:06 PM

Confirmations

6,513,608

Merkle Root

43269739fbf5ab8f13191d6806558be3903dbca82f38df76a0d45341562d6246

Transactions (1)

Coinbase43269739fbf5ab…d45341562d6246

1 in → 30 out10.0300 XPM1.06 KB

AbiApRgN…g8QuFUwL Abv8pzf1…t4zPXDTV AZawDE8P…2UydkPDF ALw8WzMm…sj2uYfgL APeshfYV…3PKcKMKH

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.

4.128 × 10⁹⁴(95-digit number)

41281621891420636760…42623840819827415039

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

4.128 × 10⁹⁴(95-digit number)

41281621891420636760…42623840819827415039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.256 × 10⁹⁴(95-digit number)

82563243782841273521…85247681639654830079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.651 × 10⁹⁵(96-digit number)

16512648756568254704…70495363279309660159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.302 × 10⁹⁵(96-digit number)

33025297513136509408…40990726558619320319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.605 × 10⁹⁵(96-digit number)

66050595026273018817…81981453117238640639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.321 × 10⁹⁶(97-digit number)

13210119005254603763…63962906234477281279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.642 × 10⁹⁶(97-digit number)

26420238010509207526…27925812468954562559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.284 × 10⁹⁶(97-digit number)

52840476021018415053…55851624937909125119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.056 × 10⁹⁷(98-digit number)

10568095204203683010…11703249875818250239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.113 × 10⁹⁷(98-digit number)

21136190408407366021…23406499751636500479

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