Block #269,349

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/23/2013, 1:21:49 AM · Difficulty 9.9536 · 6,537,662 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

003bd2a6458c37dd398d2982d1fc635bf682d7d1c0aa2a242df87ac69c5ba8e7

View on Chainz ↗

Height

#269,349

Difficulty

9.953590

Transactions

Size

2.01 KB

Version

Bits

09f41e7e

Nonce

66,009

Timestamp

11/23/2013, 1:21:49 AM

Confirmations

6,537,662

Mined by

⛏️ %aRBNATn5gfzLhrCqm3V2ysEBEDcA3mUWGXwTUs

Merkle Root

2917c07394920aeb96096080ac11657941aa98e7b6ab77de51880b135c737a3c

Transactions (1)

Coinbase2917c07394920a…880b135c737a3c

1 in → 56 out10.0600 XPM1.92 KB

ATn5gfzL…UWGXwTUs AdnG9gQ7…N9B7mA2p APZy8y6E…QZaGQjfp ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61

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.

1.010 × 10⁹³(94-digit number)

10107891231889707591…76002382012329282559

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

1.010 × 10⁹³(94-digit number)

10107891231889707591…76002382012329282559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.021 × 10⁹³(94-digit number)

20215782463779415182…52004764024658565119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.043 × 10⁹³(94-digit number)

40431564927558830364…04009528049317130239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.086 × 10⁹³(94-digit number)

80863129855117660729…08019056098634260479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.617 × 10⁹⁴(95-digit number)

16172625971023532145…16038112197268520959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.234 × 10⁹⁴(95-digit number)

32345251942047064291…32076224394537041919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.469 × 10⁹⁴(95-digit number)

64690503884094128583…64152448789074083839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.293 × 10⁹⁵(96-digit number)

12938100776818825716…28304897578148167679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.587 × 10⁹⁵(96-digit number)

25876201553637651433…56609795156296335359

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 #269,349

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