Block #294,303

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 12/4/2013, 7:35:50 PM · Difficulty 9.9910 · 6,503,565 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bd69eea6ec0b61df2c096b861a623592956322279cd1cf094de661729e30f647

View on Chainz ↗

Height

#294,303

Difficulty

9.990952

Transactions

Size

1.08 KB

Version

Bits

09fdaf0d

Nonce

321,127

Timestamp

12/4/2013, 7:35:50 PM

Confirmations

6,503,565

Mined by

⛏️ }aR^ASXXWcBr86ymQd7Qt9bp4YxwR5Vcyd82bW

Merkle Root

5fb19c76be74d46c9e96590d5fdcd7f1e472e94ac48a0439a594d8942021c581

Transactions (1)

Coinbase5fb19c76be74d4…94d8942021c581

1 in → 28 out9.9800 XPM1015 B

ASXXWcBr…Vcyd82bW AenXgLL6…ChwZjYpX AJ3bhpLE…wUY61F8E Aa9yRYxd…t5ZDhWf3 AX2fAveb…zoLMVBZ4

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.

3.864 × 10⁸⁹(90-digit number)

38641691460987541457…43803291698945387279

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

3.864 × 10⁸⁹(90-digit number)

38641691460987541457…43803291698945387279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.728 × 10⁸⁹(90-digit number)

77283382921975082915…87606583397890774559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.545 × 10⁹⁰(91-digit number)

15456676584395016583…75213166795781549119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.091 × 10⁹⁰(91-digit number)

30913353168790033166…50426333591563098239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.182 × 10⁹⁰(91-digit number)

61826706337580066332…00852667183126196479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.236 × 10⁹¹(92-digit number)

12365341267516013266…01705334366252392959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.473 × 10⁹¹(92-digit number)

24730682535032026532…03410668732504785919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.946 × 10⁹¹(92-digit number)

49461365070064053065…06821337465009571839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.892 × 10⁹¹(92-digit number)

98922730140128106131…13642674930019143679

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