Block #281,364

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/29/2013, 12:08:51 AM · Difficulty 9.9769 · 6,561,898 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5d45a4bcb76fd9a2bccd24e24b6db1ce789b57dfc8e3ef956ab1b098bbadc292

View on Chainz ↗

Height

#281,364

Difficulty

9.976851

Transactions

Size

1.01 KB

Version

Bits

09fa12ea

Nonce

154,517

Timestamp

11/29/2013, 12:08:51 AM

Confirmations

6,561,898

Mined by

⛏️ KaRfAKxUhrcXx5f5B3vqCbEaXkAJUK56oFrcLK

Merkle Root

11e42992868e377f78c5e6f4dcc7e44008bfc13ab55c97b2fcd9aded079808a4

Transactions (1)

Coinbase11e42992868e37…d9aded079808a4

1 in → 26 out10.0300 XPM947 B

AKxUhrcX…56oFrcLK AWZd1qVJ…9pj9yfPa ANKe4gqX…i5S2smrX AWGQhzDN…RDYvugUy Abn3Cpdh…D9To5DiN

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.

1.373 × 10⁹²(93-digit number)

13731130186859923293…03624182642802582559

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

1.373 × 10⁹²(93-digit number)

13731130186859923293…03624182642802582559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.746 × 10⁹²(93-digit number)

27462260373719846587…07248365285605165119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.492 × 10⁹²(93-digit number)

54924520747439693174…14496730571210330239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.098 × 10⁹³(94-digit number)

10984904149487938634…28993461142420660479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.196 × 10⁹³(94-digit number)

21969808298975877269…57986922284841320959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.393 × 10⁹³(94-digit number)

43939616597951754539…15973844569682641919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.787 × 10⁹³(94-digit number)

87879233195903509079…31947689139365283839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.757 × 10⁹⁴(95-digit number)

17575846639180701815…63895378278730567679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.515 × 10⁹⁴(95-digit number)

35151693278361403631…27790756557461135359

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

Block #281,364

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