Block #278,199

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 9:26:47 PM · Difficulty 9.9683 · 6,513,426 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bcd8b8c4a0a93cad603aa594a120fdf77a7075e8664e8be6f39bb215fe4a0c86

View on Chainz ↗

Height

#278,199

Difficulty

9.968316

Transactions

Size

1.05 KB

Version

Bits

09f7e388

Nonce

54,472

Timestamp

11/27/2013, 9:26:47 PM

Confirmations

6,513,426

Merkle Root

74cc9a67c3638f8ecada01716856d3c9923ed9eed41d39652a530f7ad24a7101

Transactions (1)

Coinbase74cc9a67c3638f…530f7ad24a7101

1 in → 27 out10.0500 XPM981 B

AbiApRgN…g8QuFUwL AbtgNzNb…9Atvu81w AN8nUzff…YcDfRDQ2 AQFgxjyj…nvZ2p9w8 AYrgZtF4…6oLCC7XK

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.

7.197 × 10⁹⁷(98-digit number)

71976866058932413861…37318268194412114389

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

7.197 × 10⁹⁷(98-digit number)

71976866058932413861…37318268194412114389

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.439 × 10⁹⁸(99-digit number)

14395373211786482772…74636536388824228779

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.879 × 10⁹⁸(99-digit number)

28790746423572965544…49273072777648457559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.758 × 10⁹⁸(99-digit number)

57581492847145931089…98546145555296915119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.151 × 10⁹⁹(100-digit number)

11516298569429186217…97092291110593830239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.303 × 10⁹⁹(100-digit number)

23032597138858372435…94184582221187660479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.606 × 10⁹⁹(100-digit number)

46065194277716744871…88369164442375320959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.213 × 10⁹⁹(100-digit number)

92130388555433489742…76738328884750641919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.842 × 10¹⁰⁰(101-digit number)

18426077711086697948…53476657769501283839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.685 × 10¹⁰⁰(101-digit number)

36852155422173395896…06953315539002567679

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