Block #249,324

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/7/2013, 9:40:28 PM · Difficulty 9.9668 · 6,541,976 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4b9b6be4e8a4ee4fd54b4ec5d5c90f44a02989c7bf258e30779d77cef7c63684

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Height

#249,324

Difficulty

9.966766

Transactions

Size

456 B

Version

Bits

09f77dfa

Nonce

32,777

Timestamp

11/7/2013, 9:40:28 PM

Confirmations

6,541,976

Merkle Root

5b7522adb0f2950f97b87f7ca7fff763394a04df1d30907ac8c5c1ebc2a87f4a

Transactions (2)

Coinbasedf4814cb1cd691…c443696b7d6447

1 in → 2 out10.0600 XPM136 B

AeL7UAFb…W9mPDyGL ALfEGCwh…VawujfMm

37124dad88d15b…91071566d8ca94

1 in → 2 out2.0909 XPM227 B

AGKU41Gn…kTFCCaNL AKbwB6o5…u33QL4yz

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.

2.832 × 10¹⁰¹(102-digit number)

28324080780225220835…34847965986491150081

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

2.832 × 10¹⁰¹(102-digit number)

28324080780225220835…34847965986491150081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.664 × 10¹⁰¹(102-digit number)

56648161560450441670…69695931972982300161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.132 × 10¹⁰²(103-digit number)

11329632312090088334…39391863945964600321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.265 × 10¹⁰²(103-digit number)

22659264624180176668…78783727891929200641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.531 × 10¹⁰²(103-digit number)

45318529248360353336…57567455783858401281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.063 × 10¹⁰²(103-digit number)

90637058496720706672…15134911567716802561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.812 × 10¹⁰³(104-digit number)

18127411699344141334…30269823135433605121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.625 × 10¹⁰³(104-digit number)

36254823398688282668…60539646270867210241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.250 × 10¹⁰³(104-digit number)

72509646797376565337…21079292541734420481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.450 × 10¹⁰⁴(105-digit number)

14501929359475313067…42158585083468840961

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer