Block #83,666

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/26/2013, 7:39:58 AM · Difficulty 9.2682 · 6,709,318 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0b3ec13943df6cb815f014d070ac50ffa65405660b96e0f1947f9644ac5c3e9e

View on Chainz ↗

Height

#83,666

Difficulty

9.268201

Transactions

Size

1.29 KB

Version

Bits

0944a8d3

Nonce

9,639

Timestamp

7/26/2013, 7:39:58 AM

Confirmations

6,709,318

Merkle Root

84170569325b2240cf92c9296e4657dcb6b1797eeebb0d3082f161d33474d84c

Transactions (2)

Coinbase7e1b46f7f0f033…21afc35fbdb009

1 in → 1 out11.6400 XPM109 B

AWQ79Gft…D8xT7RTy

3634fe2b08c8c6…45d05c908c499b

7 in → 2 out1860.1609 XPM1.09 KB

Ac8AdKzf…TguNX8ea AXMN8Vq8…xAg2x81u

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.

1.508 × 10¹⁰⁹(110-digit number)

15085060532737758129…66495797867277585099

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

1.508 × 10¹⁰⁹(110-digit number)

15085060532737758129…66495797867277585099

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.017 × 10¹⁰⁹(110-digit number)

30170121065475516259…32991595734555170199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.034 × 10¹⁰⁹(110-digit number)

60340242130951032518…65983191469110340399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.206 × 10¹¹⁰(111-digit number)

12068048426190206503…31966382938220680799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.413 × 10¹¹⁰(111-digit number)

24136096852380413007…63932765876441361599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.827 × 10¹¹⁰(111-digit number)

48272193704760826014…27865531752882723199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.654 × 10¹¹⁰(111-digit number)

96544387409521652029…55731063505765446399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.930 × 10¹¹¹(112-digit number)

19308877481904330405…11462127011530892799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.861 × 10¹¹¹(112-digit number)

38617754963808660811…22924254023061785599

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