Block #278,183

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 9:18:30 PM · Difficulty 9.9683 · 6,513,442 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2e6757299ecbc020d0cd8247d8fb2021d2b015549f717e5985621e3e0dc76067

View on Chainz ↗

Height

#278,183

Difficulty

9.968272

Transactions

Size

1.08 KB

Version

Bits

09f7e0a7

Nonce

160,174

Timestamp

11/27/2013, 9:18:30 PM

Confirmations

6,513,442

Merkle Root

5548368ca9de19f68348382d2be2eae33bd6fbd5db453a8b7521bdd5295a85a7

Transactions (1)

Coinbase5548368ca9de19…21bdd5295a85a7

1 in → 28 out10.0300 XPM1015 B

AbiApRgN…g8QuFUwL AKEwr54i…9BfmMkRh AX8aJjPq…GkydCFVo AN8nUzff…YcDfRDQ2 AZ1U8y3e…CyU6Gm24

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.

9.383 × 10⁹³(94-digit number)

93836668566976665032…27330693293426928159

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

9.383 × 10⁹³(94-digit number)

93836668566976665032…27330693293426928159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.876 × 10⁹⁴(95-digit number)

18767333713395333006…54661386586853856319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.753 × 10⁹⁴(95-digit number)

37534667426790666012…09322773173707712639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.506 × 10⁹⁴(95-digit number)

75069334853581332025…18645546347415425279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.501 × 10⁹⁵(96-digit number)

15013866970716266405…37291092694830850559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.002 × 10⁹⁵(96-digit number)

30027733941432532810…74582185389661701119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.005 × 10⁹⁵(96-digit number)

60055467882865065620…49164370779323402239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.201 × 10⁹⁶(97-digit number)

12011093576573013124…98328741558646804479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.402 × 10⁹⁶(97-digit number)

24022187153146026248…96657483117293608959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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