Block #51,081

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/16/2013, 4:10:59 AM · Difficulty 8.8930 · 6,739,864 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ed0fefa6cfb46ffc6938523931e31b1e5ea515db7a9cd7b11a4ac5f71ced1c68

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Height

#51,081

Difficulty

8.893039

Transactions

Size

199 B

Version

Bits

08e49e31

Nonce

242

Timestamp

7/16/2013, 4:10:59 AM

Confirmations

6,739,864

Merkle Root

4d01df2692fb6e20004fc31894203e4cd2293eb34a66241abf7f68d64ff8f472

Transactions (1)

Coinbase4d01df2692fb6e…7f68d64ff8f472

1 in → 1 out12.6300 XPM110 B

AeTcmmqH…LrFchfe1

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.

3.056 × 10⁹³(94-digit number)

30567573209075598038…71371842938588305239

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

3.056 × 10⁹³(94-digit number)

30567573209075598038…71371842938588305239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.113 × 10⁹³(94-digit number)

61135146418151196077…42743685877176610479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.222 × 10⁹⁴(95-digit number)

12227029283630239215…85487371754353220959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.445 × 10⁹⁴(95-digit number)

24454058567260478431…70974743508706441919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.890 × 10⁹⁴(95-digit number)

48908117134520956862…41949487017412883839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.781 × 10⁹⁴(95-digit number)

97816234269041913724…83898974034825767679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.956 × 10⁹⁵(96-digit number)

19563246853808382744…67797948069651535359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.912 × 10⁹⁵(96-digit number)

39126493707616765489…35595896139303070719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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