Block #170,291

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/18/2013, 4:12:07 PM · Difficulty 9.8655 · 6,622,287 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0b9ef710293ba644ea24fedbf43be9cd39067abacb8bc77aac15752ca29754a9

View on Chainz ↗

Height

#170,291

Difficulty

9.865513

Transactions

Size

198 B

Version

Bits

09dd9242

Nonce

82,193

Timestamp

9/18/2013, 4:12:07 PM

Confirmations

6,622,287

Merkle Root

7dfc8ff3f601770efffcdea22fd99b5d5186d2ee434338abd572ab47bb92ac1c

Transactions (1)

Coinbase7dfc8ff3f60177…72ab47bb92ac1c

1 in → 1 out10.2600 XPM109 B

AJQ7bqzh…oY2ANRaW

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.

5.813 × 10⁹²(93-digit number)

58138495559053257923…41554749998073573889

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

5.813 × 10⁹²(93-digit number)

58138495559053257923…41554749998073573889

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.162 × 10⁹³(94-digit number)

11627699111810651584…83109499996147147779

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.325 × 10⁹³(94-digit number)

23255398223621303169…66218999992294295559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.651 × 10⁹³(94-digit number)

46510796447242606338…32437999984588591119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.302 × 10⁹³(94-digit number)

93021592894485212677…64875999969177182239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.860 × 10⁹⁴(95-digit number)

18604318578897042535…29751999938354364479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.720 × 10⁹⁴(95-digit number)

37208637157794085070…59503999876708728959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.441 × 10⁹⁴(95-digit number)

74417274315588170141…19007999753417457919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.488 × 10⁹⁵(96-digit number)

14883454863117634028…38015999506834915839

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