Block #91,379

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/31/2013, 9:41:38 PM · Difficulty 9.2194 · 6,698,561 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

58b367116aff14c4cb3b9f8ec5b64bf9ec5c7ffd1eadfc7163adceececeafd7c

View on Chainz ↗

Height

#91,379

Difficulty

9.219385

Transactions

Size

205 B

Version

Bits

093829a5

Nonce

136,128

Timestamp

7/31/2013, 9:41:38 PM

Confirmations

6,698,561

Merkle Root

3fed1445131e402ee12dcdfd1e444b288470f7b98203b89ce763904c7e187f61

Transactions (1)

Coinbase3fed1445131e40…63904c7e187f61

1 in → 1 out11.7500 XPM109 B

AK1JUKWL…oPR4rN5o

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.

7.694 × 10¹⁰⁸(109-digit number)

76946139588986943481…60591424382922416281

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

7.694 × 10¹⁰⁸(109-digit number)

76946139588986943481…60591424382922416281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.538 × 10¹⁰⁹(110-digit number)

15389227917797388696…21182848765844832561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.077 × 10¹⁰⁹(110-digit number)

30778455835594777392…42365697531689665121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.155 × 10¹⁰⁹(110-digit number)

61556911671189554785…84731395063379330241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.231 × 10¹¹⁰(111-digit number)

12311382334237910957…69462790126758660481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.462 × 10¹¹⁰(111-digit number)

24622764668475821914…38925580253517320961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.924 × 10¹¹⁰(111-digit number)

49245529336951643828…77851160507034641921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.849 × 10¹¹⁰(111-digit number)

98491058673903287656…55702321014069283841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.969 × 10¹¹¹(112-digit number)

19698211734780657531…11404642028138567681

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 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 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 2CC formula:

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

Cross-reference on Chainz Explorer