Block #306,724

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/12/2013, 5:11:25 AM · Difficulty 9.9940 · 6,499,023 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9693d0fc9ae2394e34a637108ade889210eb3042b8193d77b232a9cda687fc4d

View on Chainz ↗

Height

#306,724

Difficulty

9.993962

Transactions

Size

1.15 KB

Version

Bits

09fe744b

Nonce

20,314

Timestamp

12/12/2013, 5:11:25 AM

Confirmations

6,499,023

Mined by

⛏️ $aREYAHnmt4yZ8yKykLmMEc4RwAr7pXMShoEEmi

Merkle Root

fdf3e438209092e23f1704eaf8a0af6468de14381a5d89cb5436292ab1e34073

Transactions (1)

Coinbasefdf3e438209092…36292ab1e34073

1 in → 30 out9.9800 XPM1.06 KB

AHnmt4yZ…MShoEEmi AG5YAjec…VhA4Aeh1 Acs9SHrk…QJSB8SFG Ad9pSzHt…cpJ3y2zz AWA5FEzr…x9RdPKTy

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.

3.069 × 10⁹³(94-digit number)

30699588642408758575…59963299727430206081

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

3.069 × 10⁹³(94-digit number)

30699588642408758575…59963299727430206081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.139 × 10⁹³(94-digit number)

61399177284817517151…19926599454860412161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.227 × 10⁹⁴(95-digit number)

12279835456963503430…39853198909720824321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.455 × 10⁹⁴(95-digit number)

24559670913927006860…79706397819441648641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.911 × 10⁹⁴(95-digit number)

49119341827854013721…59412795638883297281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.823 × 10⁹⁴(95-digit number)

98238683655708027442…18825591277766594561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.964 × 10⁹⁵(96-digit number)

19647736731141605488…37651182555533189121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.929 × 10⁹⁵(96-digit number)

39295473462283210977…75302365111066378241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.859 × 10⁹⁵(96-digit number)

78590946924566421954…50604730222132756481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.571 × 10⁹⁶(97-digit number)

15718189384913284390…01209460444265512961

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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