Block #344,412

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/5/2014, 7:14:40 AM · Difficulty 10.1929 · 6,449,782 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e69bb2f5933e33adac4da888bb635069b0c0fc9dd9ebad8a9f7ac46f3332d634

View on Chainz ↗

Height

#344,412

Difficulty

10.192935

Transactions

Size

3.01 KB

Version

Bits

0a316428

Nonce

133,864

Timestamp

1/5/2014, 7:14:40 AM

Confirmations

6,449,782

Merkle Root

f273dd2277e19bc96eb2fc427c8ef2e171ac81ed1bd635157189f6879f78c7ec

Transactions (2)

Coinbase7d837631dde3fa…1a6489b65695c1

1 in → 24 out9.6100 XPM879 B

AP5UvYhU…vLTDwkdA AGtTZ216…MBnuPteD AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AZV4TwxQ…8JnQqSoH

c3066112f210e3…c0d5d7afcae871

14 in → 1 out500.0000 XPM2.07 KB

AJjnK9uC…VreFquR4

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.

2.176 × 10⁹⁰(91-digit number)

21761323279200931781…41784415282126407399

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

2.176 × 10⁹⁰(91-digit number)

21761323279200931781…41784415282126407399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.352 × 10⁹⁰(91-digit number)

43522646558401863562…83568830564252814799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.704 × 10⁹⁰(91-digit number)

87045293116803727125…67137661128505629599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.740 × 10⁹¹(92-digit number)

17409058623360745425…34275322257011259199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.481 × 10⁹¹(92-digit number)

34818117246721490850…68550644514022518399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.963 × 10⁹¹(92-digit number)

69636234493442981700…37101289028045036799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.392 × 10⁹²(93-digit number)

13927246898688596340…74202578056090073599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.785 × 10⁹²(93-digit number)

27854493797377192680…48405156112180147199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.570 × 10⁹²(93-digit number)

55708987594754385360…96810312224360294399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.114 × 10⁹³(94-digit number)

11141797518950877072…93620624448720588799

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