Block #182,331

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/27/2013, 5:38:30 AM · Difficulty 9.8587 · 6,627,321 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

225365fdacc4c144d9ede780d1bdc5813e54081b994b4247cc7a0ac397b2063f

View on Chainz ↗

Height

#182,331

Difficulty

9.858686

Transactions

Size

395 B

Version

Bits

09dbd2dc

Nonce

169,080

Timestamp

9/27/2013, 5:38:30 AM

Confirmations

6,627,321

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

290918280da12d14fb1d8299fa2f7a47ac48c929f070489487fbce17ce3d4b0a

Transactions (2)

Coinbase2669c9fa40aa4e…da2f157fe439c6

1 in → 1 out10.2829 XPM109 B

AWbQMT1U…8Pt4ow7J

c2e0b5907be2b7…076c8b0d2342f8

1 in → 1 out13.6000 XPM193 B

AP4G5Aiy…MZgQSmXp

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.

1.430 × 10¹⁰²(103-digit number)

14301291105978053767…79686925882373144959

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

1.430 × 10¹⁰²(103-digit number)

14301291105978053767…79686925882373144959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.860 × 10¹⁰²(103-digit number)

28602582211956107534…59373851764746289919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.720 × 10¹⁰²(103-digit number)

57205164423912215069…18747703529492579839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.144 × 10¹⁰³(104-digit number)

11441032884782443013…37495407058985159679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.288 × 10¹⁰³(104-digit number)

22882065769564886027…74990814117970319359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.576 × 10¹⁰³(104-digit number)

45764131539129772055…49981628235940638719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.152 × 10¹⁰³(104-digit number)

91528263078259544110…99963256471881277439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.830 × 10¹⁰⁴(105-digit number)

18305652615651908822…99926512943762554879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.661 × 10¹⁰⁴(105-digit number)

36611305231303817644…99853025887525109759

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 #182,331

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