Block #278,073

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 8:18:42 PM · Difficulty 9.9679 · 6,514,701 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1be14fbdd632cd8d2fcec82d69c60bfedf82ba4e5869deabffe523ccb0a8d171

View on Chainz ↗

Height

#278,073

Difficulty

9.967946

Transactions

Size

1.08 KB

Version

Bits

09f7cb53

Nonce

271,501

Timestamp

11/27/2013, 8:18:42 PM

Confirmations

6,514,701

Merkle Root

9d28f7e557ea61680abaf212a0b1a1a8e459b67b63c67712973c7c09ac3d4604

Transactions (1)

Coinbase9d28f7e557ea61…3c7c09ac3d4604

1 in → 28 out10.0300 XPM1015 B

AbiApRgN…g8QuFUwL AS6sRu1R…UpJKwm5m AGAf8Z9Q…ggDWo52w AHfwsMTb…pY1MpjeT AayReikY…2HAC42fs

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.

3.920 × 10⁹²(93-digit number)

39208098837112124006…00557202937411302399

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

3.920 × 10⁹²(93-digit number)

39208098837112124006…00557202937411302399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.841 × 10⁹²(93-digit number)

78416197674224248013…01114405874822604799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.568 × 10⁹³(94-digit number)

15683239534844849602…02228811749645209599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.136 × 10⁹³(94-digit number)

31366479069689699205…04457623499290419199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.273 × 10⁹³(94-digit number)

62732958139379398410…08915246998580838399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.254 × 10⁹⁴(95-digit number)

12546591627875879682…17830493997161676799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.509 × 10⁹⁴(95-digit number)

25093183255751759364…35660987994323353599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.018 × 10⁹⁴(95-digit number)

50186366511503518728…71321975988646707199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.003 × 10⁹⁵(96-digit number)

10037273302300703745…42643951977293414399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.007 × 10⁹⁵(96-digit number)

20074546604601407491…85287903954586828799

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