Block #344,558

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/5/2014, 9:18:07 AM · Difficulty 10.1961 · 6,457,676 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6c2afe018878cbc6808081326fab796ed1d326fd439d7a9dcab14250b4705a1e

View on Chainz ↗

Height

#344,558

Difficulty

10.196088

Transactions

Size

1.05 KB

Version

Bits

0a3232d9

Nonce

369,652

Timestamp

1/5/2014, 9:18:07 AM

Confirmations

6,457,676

Mined by

⛏️ AaR#|AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3009182083fba3517b53fddaa14923a5f119118c49caba423e40c2c43af84c06

Transactions (1)

Coinbase3009182083fba3…40c2c43af84c06

1 in → 27 out9.5793 XPM981 B

AQvZBsUo…hppgRZTJ AZemWJAo…6jhDtieG AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AWQyM49v…zN9UeNMm

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.

7.426 × 10¹⁰²(103-digit number)

74265257508522656215…60605871950685839359

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

7.426 × 10¹⁰²(103-digit number)

74265257508522656215…60605871950685839359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.485 × 10¹⁰³(104-digit number)

14853051501704531243…21211743901371678719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.970 × 10¹⁰³(104-digit number)

29706103003409062486…42423487802743357439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.941 × 10¹⁰³(104-digit number)

59412206006818124972…84846975605486714879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.188 × 10¹⁰⁴(105-digit number)

11882441201363624994…69693951210973429759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.376 × 10¹⁰⁴(105-digit number)

23764882402727249989…39387902421946859519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.752 × 10¹⁰⁴(105-digit number)

47529764805454499978…78775804843893719039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.505 × 10¹⁰⁴(105-digit number)

95059529610908999956…57551609687787438079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.901 × 10¹⁰⁵(106-digit number)

19011905922181799991…15103219375574876159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.802 × 10¹⁰⁵(106-digit number)

38023811844363599982…30206438751149752319

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