Block #189,207

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/1/2013, 4:17:19 PM · Difficulty 9.8725 · 6,604,028 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6dd7e119caed3d0d8acccae1394763416a3ee1e3aa99ce49360a46296689b38a

View on Chainz ↗

Height

#189,207

Difficulty

9.872477

Transactions

Size

197 B

Version

Bits

09df5aa6

Nonce

176,827

Timestamp

10/1/2013, 4:17:19 PM

Confirmations

6,604,028

Merkle Root

a223018b6c9f5ece9ead3b895cd73a4859b5873ce79e3aef7bf1b122d720cd08

Transactions (1)

Coinbasea223018b6c9f5e…f1b122d720cd08

1 in → 1 out10.2400 XPM109 B

ARsxB1G4…moBvdb8v

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.

4.221 × 10⁸⁹(90-digit number)

42212150476335630380…17979663797657970879

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

4.221 × 10⁸⁹(90-digit number)

42212150476335630380…17979663797657970879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.442 × 10⁸⁹(90-digit number)

84424300952671260760…35959327595315941759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.688 × 10⁹⁰(91-digit number)

16884860190534252152…71918655190631883519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.376 × 10⁹⁰(91-digit number)

33769720381068504304…43837310381263767039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.753 × 10⁹⁰(91-digit number)

67539440762137008608…87674620762527534079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.350 × 10⁹¹(92-digit number)

13507888152427401721…75349241525055068159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.701 × 10⁹¹(92-digit number)

27015776304854803443…50698483050110136319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.403 × 10⁹¹(92-digit number)

54031552609709606886…01396966100220272639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.080 × 10⁹²(93-digit number)

10806310521941921377…02793932200440545279

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