Block #463,768

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/28/2014, 8:49:06 AM · Difficulty 10.4138 · 6,342,563 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f108518c3a22565ff6171fadc19c8100345d1dcc694633060c2247ce9dc2a975

View on Chainz ↗

Height

#463,768

Difficulty

10.413769

Transactions

Size

935 B

Version

Bits

0a69ecc8

Nonce

11,084

Timestamp

3/28/2014, 8:49:06 AM

Confirmations

6,342,563

Mined by

⛏️ aS57AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

63c6cf6255d97fa6caea9baae651e469516f2bbb9884576233dfc91a558f9052

Transactions (1)

Coinbase63c6cf6255d97f…dfc91a558f9052

1 in → 23 out9.2100 XPM845 B

AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR AJtNW28X…Syb4Ph5j ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

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.

8.860 × 10⁹³(94-digit number)

88601594681481640834…59024935347864170639

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

8.860 × 10⁹³(94-digit number)

88601594681481640834…59024935347864170639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.772 × 10⁹⁴(95-digit number)

17720318936296328166…18049870695728341279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.544 × 10⁹⁴(95-digit number)

35440637872592656333…36099741391456682559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.088 × 10⁹⁴(95-digit number)

70881275745185312667…72199482782913365119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.417 × 10⁹⁵(96-digit number)

14176255149037062533…44398965565826730239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.835 × 10⁹⁵(96-digit number)

28352510298074125066…88797931131653460479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.670 × 10⁹⁵(96-digit number)

56705020596148250133…77595862263306920959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.134 × 10⁹⁶(97-digit number)

11341004119229650026…55191724526613841919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.268 × 10⁹⁶(97-digit number)

22682008238459300053…10383449053227683839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.536 × 10⁹⁶(97-digit number)

45364016476918600107…20766898106455367679

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 #463,768

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