Block #520,026

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/1/2014, 2:44:59 PM · Difficulty 10.8574 · 6,294,189 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

590509e89f5f15337316d2843934838796682aa1e4a694a4cafbfb99cbb769b6

View on Chainz ↗

Height

#520,026

Difficulty

10.857396

Transactions

Size

211 B

Version

Bits

0adb7e52

Nonce

67,146,888

Timestamp

5/1/2014, 2:44:59 PM

Confirmations

6,294,189

Mined by

⛏️ P2SHAGRrLX34WgfnJ9WqPzqMcrNb8GF9zbreRe

Merkle Root

812c6bc7a5208c5a027153a7eafb926714d6ae30e97e094de282a5eda04f0c67

Transactions (1)

Coinbase812c6bc7a5208c…82a5eda04f0c67

1 in → 1 out8.4700 XPM118 B

AGRrLX34…F9zbreRe

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.

1.510 × 10¹⁰¹(102-digit number)

15105948356464305676…28577925411074682879

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

1.510 × 10¹⁰¹(102-digit number)

15105948356464305676…28577925411074682879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.021 × 10¹⁰¹(102-digit number)

30211896712928611353…57155850822149365759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.042 × 10¹⁰¹(102-digit number)

60423793425857222707…14311701644298731519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.208 × 10¹⁰²(103-digit number)

12084758685171444541…28623403288597463039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.416 × 10¹⁰²(103-digit number)

24169517370342889082…57246806577194926079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.833 × 10¹⁰²(103-digit number)

48339034740685778165…14493613154389852159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.667 × 10¹⁰²(103-digit number)

96678069481371556331…28987226308779704319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.933 × 10¹⁰³(104-digit number)

19335613896274311266…57974452617559408639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.867 × 10¹⁰³(104-digit number)

38671227792548622532…15948905235118817279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.734 × 10¹⁰³(104-digit number)

77342455585097245065…31897810470237634559

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 #520,026

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