Block #349,815

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/8/2014, 3:25:35 PM · Difficulty 10.2834 · 6,456,435 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e002ed6ab07340376c2a5ce587fe2d63b25806bc8216ee90e681aa4c5f8d084b

View on Chainz ↗

Height

#349,815

Difficulty

10.283416

Transactions

Size

209 B

Version

Bits

0a488df9

Nonce

133,291

Timestamp

1/8/2014, 3:25:35 PM

Confirmations

6,456,435

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ea355d5dc47e55ca9bb1e3a8bc4340ee2244e5b5ef4a2b407606d252d7ff6c99

Transactions (1)

Coinbaseea355d5dc47e55…06d252d7ff6c99

1 in → 1 out9.4400 XPM116 B

AbwWkWZt…kawDhufa

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.

6.847 × 10¹⁰⁰(101-digit number)

68474295436007247609…94455280831884921639

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

6.847 × 10¹⁰⁰(101-digit number)

68474295436007247609…94455280831884921639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.369 × 10¹⁰¹(102-digit number)

13694859087201449521…88910561663769843279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.738 × 10¹⁰¹(102-digit number)

27389718174402899043…77821123327539686559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.477 × 10¹⁰¹(102-digit number)

54779436348805798087…55642246655079373119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.095 × 10¹⁰²(103-digit number)

10955887269761159617…11284493310158746239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.191 × 10¹⁰²(103-digit number)

21911774539522319235…22568986620317492479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.382 × 10¹⁰²(103-digit number)

43823549079044638470…45137973240634984959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.764 × 10¹⁰²(103-digit number)

87647098158089276940…90275946481269969919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.752 × 10¹⁰³(104-digit number)

17529419631617855388…80551892962539939839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.505 × 10¹⁰³(104-digit number)

35058839263235710776…61103785925079879679

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 #349,815

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