Block #244,127

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/4/2013, 4:43:06 PM · Difficulty 9.9625 · 6,587,962 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7c139ee58bc7670a7672e6d14d26005008c6cd385c46ad94d1a3303ca1c63af7

View on Chainz ↗

Height

#244,127

Difficulty

9.962479

Transactions

Size

1.64 KB

Version

Bits

09f66500

Nonce

243,808

Timestamp

11/4/2013, 4:43:06 PM

Confirmations

6,587,962

Mined by

⛏️ RwsAGmDpQMh59CnnHC5hkWNpHPQHF8qfUtstd

Merkle Root

8d31885a3ed5a8afeadce0159365d8855c35390a9d617e9b0ad483dc59619c84

Transactions (1)

Coinbase8d31885a3ed5a8…d483dc59619c84

1 in → 45 out10.0400 XPM1.55 KB

AGmDpQMh…8qfUtstd ANUaggy4…MWdrertQ ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AZWiC56x…NwextJca

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.

1.071 × 10⁹⁰(91-digit number)

10716578817293237817…04798863724712083999

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

1.071 × 10⁹⁰(91-digit number)

10716578817293237817…04798863724712083999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.143 × 10⁹⁰(91-digit number)

21433157634586475634…09597727449424167999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.286 × 10⁹⁰(91-digit number)

42866315269172951269…19195454898848335999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.573 × 10⁹⁰(91-digit number)

85732630538345902538…38390909797696671999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.714 × 10⁹¹(92-digit number)

17146526107669180507…76781819595393343999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.429 × 10⁹¹(92-digit number)

34293052215338361015…53563639190786687999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.858 × 10⁹¹(92-digit number)

68586104430676722030…07127278381573375999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.371 × 10⁹²(93-digit number)

13717220886135344406…14254556763146751999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.743 × 10⁹²(93-digit number)

27434441772270688812…28509113526293503999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.486 × 10⁹²(93-digit number)

54868883544541377624…57018227052587007999

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

Block #244,127

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