Block #195,089

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/5/2013, 1:44:16 PM · Difficulty 9.8802 · 6,594,742 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2b7153509025c3ccc0b2f772479d7b0ea54418f6a5f63740eb92b3c83aa6e0ee

View on Chainz ↗

Height

#195,089

Difficulty

9.880224

Transactions

Size

200 B

Version

Bits

09e1565d

Nonce

108,740

Timestamp

10/5/2013, 1:44:16 PM

Confirmations

6,594,742

Merkle Root

20152455e61a2b3a585e02e48339c133d9c8c5e7b57cb29dd7f8805236158ef8

Transactions (1)

Coinbase20152455e61a2b…f8805236158ef8

1 in → 1 out10.2300 XPM109 B

AZv7gMUK…CbiASjGW

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.

2.435 × 10⁹⁸(99-digit number)

24355565651447190507…19888875263127347199

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

2.435 × 10⁹⁸(99-digit number)

24355565651447190507…19888875263127347199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.871 × 10⁹⁸(99-digit number)

48711131302894381014…39777750526254694399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.742 × 10⁹⁸(99-digit number)

97422262605788762029…79555501052509388799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.948 × 10⁹⁹(100-digit number)

19484452521157752405…59111002105018777599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.896 × 10⁹⁹(100-digit number)

38968905042315504811…18222004210037555199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.793 × 10⁹⁹(100-digit number)

77937810084631009623…36444008420075110399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.558 × 10¹⁰⁰(101-digit number)

15587562016926201924…72888016840150220799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.117 × 10¹⁰⁰(101-digit number)

31175124033852403849…45776033680300441599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.235 × 10¹⁰⁰(101-digit number)

62350248067704807698…91552067360600883199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.247 × 10¹⁰¹(102-digit number)

12470049613540961539…83104134721201766399

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