Block #72,327

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/20/2013, 11:28:41 PM · Difficulty 8.9940 · 6,717,708 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0292a93087541480624ed04d52261f6d4d9564dc67ea161832d589e4779c0741

View on Chainz ↗

Height

#72,327

Difficulty

8.993982

Transactions

Size

769 B

Version

Bits

08fe7599

Nonce

1,520

Timestamp

7/20/2013, 11:28:41 PM

Confirmations

6,717,708

Merkle Root

1aa7187df5bf5b9fc6f6dda01eb90200605f4786a650f111595133ba6d9ec6ed

Transactions (2)

Coinbase28e79c4e5a40b5…d21f561d56d80f

1 in → 1 out12.3500 XPM110 B

AY23v3dx…w8m65ARr

6674755cab491e…37df137ff554ef

4 in → 1 out49.4500 XPM568 B

AJ5JDkMB…S91bdMiR

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.

1.722 × 10⁹⁷(98-digit number)

17224273024133330179…90293839510410765581

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

1.722 × 10⁹⁷(98-digit number)

17224273024133330179…90293839510410765581

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.444 × 10⁹⁷(98-digit number)

34448546048266660358…80587679020821531161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.889 × 10⁹⁷(98-digit number)

68897092096533320716…61175358041643062321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.377 × 10⁹⁸(99-digit number)

13779418419306664143…22350716083286124641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.755 × 10⁹⁸(99-digit number)

27558836838613328286…44701432166572249281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.511 × 10⁹⁸(99-digit number)

55117673677226656573…89402864333144498561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.102 × 10⁹⁹(100-digit number)

11023534735445331314…78805728666288997121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.204 × 10⁹⁹(100-digit number)

22047069470890662629…57611457332577994241

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second 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 8

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer