Block #50,843

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/16/2013, 3:10:28 AM · Difficulty 8.8892 · 6,741,156 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8f04363281df3c860aaea4f99d375f877599ac5472708a22440d5a0221b26b6d

View on Chainz ↗

Height

#50,843

Difficulty

8.889191

Transactions

Size

203 B

Version

Bits

08e3a20b

Nonce

146

Timestamp

7/16/2013, 3:10:28 AM

Confirmations

6,741,156

Merkle Root

dedbd0fd93519cb29a8b792394674b500ae9140eeaee88a4e0e174574405ceea

Transactions (1)

Coinbasededbd0fd93519c…e174574405ceea

1 in → 1 out12.6400 XPM110 B

AeTcmmqH…LrFchfe1

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.

2.172 × 10¹⁰¹(102-digit number)

21723939538503674510…87108883171973156139

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

2.172 × 10¹⁰¹(102-digit number)

21723939538503674510…87108883171973156139

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.344 × 10¹⁰¹(102-digit number)

43447879077007349021…74217766343946312279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.689 × 10¹⁰¹(102-digit number)

86895758154014698042…48435532687892624559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.737 × 10¹⁰²(103-digit number)

17379151630802939608…96871065375785249119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.475 × 10¹⁰²(103-digit number)

34758303261605879217…93742130751570498239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.951 × 10¹⁰²(103-digit number)

69516606523211758434…87484261503140996479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.390 × 10¹⁰³(104-digit number)

13903321304642351686…74968523006281992959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.780 × 10¹⁰³(104-digit number)

27806642609284703373…49937046012563985919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.561 × 10¹⁰³(104-digit number)

55613285218569406747…99874092025127971839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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