Block #241,284

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/3/2013, 3:08:27 AM · Difficulty 9.9577 · 6,553,053 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b3f9bd7213e1d8a02ca1aa6b4cff1001de3e44842062028f5fb148aa86e9e017

View on Chainz ↗

Height

#241,284

Difficulty

9.957700

Transactions

Size

1.97 KB

Version

Bits

09f52bcf

Nonce

152,102

Timestamp

11/3/2013, 3:08:27 AM

Confirmations

6,553,053

Merkle Root

9ff343242ea1a266c013ebf2c4809e077da3ccf5577dd6531369c7e40f36e752

Transactions (1)

Coinbase9ff343242ea1a2…69c7e40f36e752

1 in → 55 out10.0500 XPM1.89 KB

ARjgNH4d…BU7Drh7C AQtzUSwq…htAuF3yC AZWiC56x…NwextJca AcEnwywz…vZtt2xTs AKDTDDtx…iqvw9cdY

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.

2.692 × 10⁹⁰(91-digit number)

26924129757673107516…67689680820962457119

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

2.692 × 10⁹⁰(91-digit number)

26924129757673107516…67689680820962457119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.384 × 10⁹⁰(91-digit number)

53848259515346215033…35379361641924914239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.076 × 10⁹¹(92-digit number)

10769651903069243006…70758723283849828479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.153 × 10⁹¹(92-digit number)

21539303806138486013…41517446567699656959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.307 × 10⁹¹(92-digit number)

43078607612276972027…83034893135399313919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.615 × 10⁹¹(92-digit number)

86157215224553944054…66069786270798627839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.723 × 10⁹²(93-digit number)

17231443044910788810…32139572541597255679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.446 × 10⁹²(93-digit number)

34462886089821577621…64279145083194511359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.892 × 10⁹²(93-digit number)

68925772179643155243…28558290166389022719

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