Block #84,677

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/26/2013, 11:46:54 PM · Difficulty 9.2750 · 6,706,741 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

44670416dfa7bae513c6dd7bfec95c12df10cd76ac6598a52bd63206bb10c6ec

View on Chainz ↗

Height

#84,677

Difficulty

9.274964

Transactions

Size

205 B

Version

Bits

0946640d

Nonce

236,588

Timestamp

7/26/2013, 11:46:54 PM

Confirmations

6,706,741

Merkle Root

8c65038073d84153b7fa6c55c7f410d2cb7814c2123474e18175faa5e024956d

Transactions (1)

Coinbase8c65038073d841…75faa5e024956d

1 in → 1 out11.6100 XPM109 B

AcuJraLT…Y66BS47Q

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.

2.567 × 10¹⁰⁹(110-digit number)

25674141951901520373…71986695407724146399

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

2.567 × 10¹⁰⁹(110-digit number)

25674141951901520373…71986695407724146399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.134 × 10¹⁰⁹(110-digit number)

51348283903803040747…43973390815448292799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.026 × 10¹¹⁰(111-digit number)

10269656780760608149…87946781630896585599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.053 × 10¹¹⁰(111-digit number)

20539313561521216298…75893563261793171199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.107 × 10¹¹⁰(111-digit number)

41078627123042432597…51787126523586342399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.215 × 10¹¹⁰(111-digit number)

82157254246084865195…03574253047172684799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.643 × 10¹¹¹(112-digit number)

16431450849216973039…07148506094345369599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.286 × 10¹¹¹(112-digit number)

32862901698433946078…14297012188690739199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.572 × 10¹¹¹(112-digit number)

65725803396867892156…28594024377381478399

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