Block #44,659

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/15/2013, 12:20:01 AM · Difficulty 8.7251 · 6,747,567 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

be929731c8fa436cdccf5a5e57ae70d2ce412d22d3fd17e03903a9b4360a62f2

View on Chainz ↗

Height

#44,659

Difficulty

8.725135

Transactions

Size

204 B

Version

Bits

08b9a26d

Nonce

Timestamp

7/15/2013, 12:20:01 AM

Confirmations

6,747,567

Merkle Root

2ac70c6a5b362e210afb04a67c62cc588c488a4c0653ab2a71fd56cf44049df1

Transactions (1)

Coinbase2ac70c6a5b362e…fd56cf44049df1

1 in → 1 out13.1200 XPM110 B

AHyQPhVN…oSMZDzL1

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.

2.815 × 10¹⁰³(104-digit number)

28158546739483595656…55683095240834408719

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

2.815 × 10¹⁰³(104-digit number)

28158546739483595656…55683095240834408719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.631 × 10¹⁰³(104-digit number)

56317093478967191313…11366190481668817439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.126 × 10¹⁰⁴(105-digit number)

11263418695793438262…22732380963337634879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.252 × 10¹⁰⁴(105-digit number)

22526837391586876525…45464761926675269759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.505 × 10¹⁰⁴(105-digit number)

45053674783173753051…90929523853350539519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.010 × 10¹⁰⁴(105-digit number)

90107349566347506102…81859047706701079039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.802 × 10¹⁰⁵(106-digit number)

18021469913269501220…63718095413402158079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.604 × 10¹⁰⁵(106-digit number)

36042939826539002440…27436190826804316159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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