Block #341,244

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/3/2014, 8:15:44 AM · Difficulty 10.1344 · 6,462,693 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

65795e69f13d6bec7b7c1c4287652c563863eac29168fbb380f0ff6d42104e24

View on Chainz ↗

Height

#341,244

Difficulty

10.134370

Transactions

Size

1.11 KB

Version

Bits

0a22661a

Nonce

157,660

Timestamp

1/3/2014, 8:15:44 AM

Confirmations

6,462,693

Mined by

⛏️ 4aRqoAQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

38dd8c89fa7748257604f6d4fbb6c1ee11396c7304084bf56ebb473bbc5b6299

Transactions (1)

Coinbase38dd8c89fa7748…bb473bbc5b6299

1 in → 29 out9.7000 XPM1.02 KB

AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 AcV2etJ3…AC6C3Zed AP5UvYhU…vLTDwkdA AMR1zc5T…bj5fokRu

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.

1.137 × 10⁹⁴(95-digit number)

11378797393444547043…75390040099006544159

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

1.137 × 10⁹⁴(95-digit number)

11378797393444547043…75390040099006544159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.275 × 10⁹⁴(95-digit number)

22757594786889094086…50780080198013088319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.551 × 10⁹⁴(95-digit number)

45515189573778188172…01560160396026176639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.103 × 10⁹⁴(95-digit number)

91030379147556376344…03120320792052353279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.820 × 10⁹⁵(96-digit number)

18206075829511275268…06240641584104706559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.641 × 10⁹⁵(96-digit number)

36412151659022550537…12481283168209413119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.282 × 10⁹⁵(96-digit number)

72824303318045101075…24962566336418826239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.456 × 10⁹⁶(97-digit number)

14564860663609020215…49925132672837652479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.912 × 10⁹⁶(97-digit number)

29129721327218040430…99850265345675304959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.825 × 10⁹⁶(97-digit number)

58259442654436080860…99700530691350609919

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