Block #279,327

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/28/2013, 7:43:15 AM · Difficulty 9.9714 · 6,537,625 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

75778cb9b0b1c66fc21f02c6c81a610df347fd9eb6ea2bf55ad34d0471d498f6

View on Chainz ↗

Height

#279,327

Difficulty

9.971407

Transactions

Size

1.08 KB

Version

Bits

09f8ae1d

Nonce

6,418

Timestamp

11/28/2013, 7:43:15 AM

Confirmations

6,537,625

Mined by

⛏️ CaRdAN8nUzffzPFGV1c5CDiMhELQSRYcDfRDQ2

Merkle Root

cd5529bab7f4067d3051e87f1571b552f11f49e1369de228c9b333a895af90c0

Transactions (1)

Coinbasecd5529bab7f406…b333a895af90c0

1 in → 28 out10.0200 XPM1015 B

AN8nUzff…YcDfRDQ2 APVGazMT…cDCk2nwA AScAzqGc…BZ6tV1vJ AaN3X4nJ…7DX2KLvh Ac5sZcdP…kzV4eckG

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.

1.042 × 10⁹⁴(95-digit number)

10429860272135105167…15062043723205442879

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

1.042 × 10⁹⁴(95-digit number)

10429860272135105167…15062043723205442879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.085 × 10⁹⁴(95-digit number)

20859720544270210334…30124087446410885759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.171 × 10⁹⁴(95-digit number)

41719441088540420668…60248174892821771519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.343 × 10⁹⁴(95-digit number)

83438882177080841337…20496349785643543039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.668 × 10⁹⁵(96-digit number)

16687776435416168267…40992699571287086079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.337 × 10⁹⁵(96-digit number)

33375552870832336534…81985399142574172159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.675 × 10⁹⁵(96-digit number)

66751105741664673069…63970798285148344319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.335 × 10⁹⁶(97-digit number)

13350221148332934613…27941596570296688639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.670 × 10⁹⁶(97-digit number)

26700442296665869227…55883193140593377279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.340 × 10⁹⁶(97-digit number)

53400884593331738455…11766386281186754559

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

Block #279,327

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