Block #238,719

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/1/2013, 5:00:12 PM · Difficulty 9.9530 · 6,554,061 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2010a5cc543db9b98893f98e1e1c143b4db0e430a225de614029987e93eca257

View on Chainz ↗

Height

#238,719

Difficulty

9.953024

Transactions

Size

1.16 KB

Version

Bits

09f3f95a

Nonce

19,407

Timestamp

11/1/2013, 5:00:12 PM

Confirmations

6,554,061

Merkle Root

0521429c9275db77ea7d1e1b95ea1f108ab8a87ebe485400024069888951759d

Transactions (2)

Coinbase9c24d10d5a7392…75fa3d7ebf4dfe

1 in → 1 out10.0900 XPM109 B

AdvNHsXX…1mgsgfsd

0cf575bf838b95…f468f094ce15c9

8 in → 2 out80.9800 XPM992 B

AZDw8GgW…GexTkqVt AVWBnwrc…1cicukg2

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.

2.261 × 10⁹¹(92-digit number)

22614190411286869964…02916771288761113919

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

2.261 × 10⁹¹(92-digit number)

22614190411286869964…02916771288761113919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.522 × 10⁹¹(92-digit number)

45228380822573739928…05833542577522227839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.045 × 10⁹¹(92-digit number)

90456761645147479857…11667085155044455679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.809 × 10⁹²(93-digit number)

18091352329029495971…23334170310088911359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.618 × 10⁹²(93-digit number)

36182704658058991943…46668340620177822719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.236 × 10⁹²(93-digit number)

72365409316117983886…93336681240355645439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.447 × 10⁹³(94-digit number)

14473081863223596777…86673362480711290879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.894 × 10⁹³(94-digit number)

28946163726447193554…73346724961422581759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.789 × 10⁹³(94-digit number)

57892327452894387109…46693449922845163519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.157 × 10⁹⁴(95-digit number)

11578465490578877421…93386899845690327039

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