Block #125,538

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/20/2013, 7:48:36 AM · Difficulty 9.7769 · 6,689,567 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d0abc617e606c7b45b9e2c3d66556ad90d2635bad270cca4df8b33f23068f87b

View on Chainz ↗

Height

#125,538

Difficulty

9.776930

Transactions

Size

201 B

Version

Bits

09c6e4e4

Nonce

77,790

Timestamp

8/20/2013, 7:48:36 AM

Confirmations

6,689,567

Mined by

⛏️ P2SHASki8pmAYiSmpQcpe6L3Yu14B9Dwetzr7b

Merkle Root

aaa2e2d23e4cdbccf97043b9803fbfc960848533f2ca7cce377424a885b65ec8

Transactions (1)

Coinbaseaaa2e2d23e4cdb…7424a885b65ec8

1 in → 1 out10.4500 XPM109 B

ASki8pmA…Dwetzr7b

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.

1.723 × 10⁹⁹(100-digit number)

17232964833953092992…49942290375404688299

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

1.723 × 10⁹⁹(100-digit number)

17232964833953092992…49942290375404688299

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.446 × 10⁹⁹(100-digit number)

34465929667906185984…99884580750809376599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.893 × 10⁹⁹(100-digit number)

68931859335812371969…99769161501618753199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.378 × 10¹⁰⁰(101-digit number)

13786371867162474393…99538323003237506399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.757 × 10¹⁰⁰(101-digit number)

27572743734324948787…99076646006475012799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.514 × 10¹⁰⁰(101-digit number)

55145487468649897575…98153292012950025599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.102 × 10¹⁰¹(102-digit number)

11029097493729979515…96306584025900051199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.205 × 10¹⁰¹(102-digit number)

22058194987459959030…92613168051800102399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.411 × 10¹⁰¹(102-digit number)

44116389974919918060…85226336103600204799

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 #125,538

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