Block #306,620

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/12/2013, 3:46:34 AM · Difficulty 9.9939 · 6,496,434 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d95e1c9b31bf2779a4b3ff994a1fc18ba15c8247f5756cc5356b7948a750686b

View on Chainz ↗

Height

#306,620

Difficulty

9.993935

Transactions

Size

1.18 KB

Version

Bits

09fe727e

Nonce

60,091

Timestamp

12/12/2013, 3:46:34 AM

Confirmations

6,496,434

Mined by

⛏️ aR1ARcqMJhpYZE2kngc2mc4PFnwnaRVLToQ6S

Merkle Root

3e7562f3746e9b9318fe9d7d1d555d2472c5993da8cb2c17cfe815fdce7a741e

Transactions (1)

Coinbase3e7562f3746e9b…e815fdce7a741e

1 in → 31 out9.9800 XPM1.09 KB

ARcqMJhp…RVLToQ6S AJzWx2VD…j4ZSMit5 AG5YAjec…VhA4Aeh1 APkLnQkh…8dTBJfQ6 AVo65BNV…rnDcddTj

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.

1.199 × 10⁹⁵(96-digit number)

11990873556303871385…88401525605963163001

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

1.199 × 10⁹⁵(96-digit number)

11990873556303871385…88401525605963163001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.398 × 10⁹⁵(96-digit number)

23981747112607742770…76803051211926326001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.796 × 10⁹⁵(96-digit number)

47963494225215485541…53606102423852652001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.592 × 10⁹⁵(96-digit number)

95926988450430971083…07212204847705304001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.918 × 10⁹⁶(97-digit number)

19185397690086194216…14424409695410608001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.837 × 10⁹⁶(97-digit number)

38370795380172388433…28848819390821216001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.674 × 10⁹⁶(97-digit number)

76741590760344776867…57697638781642432001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.534 × 10⁹⁷(98-digit number)

15348318152068955373…15395277563284864001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.069 × 10⁹⁷(98-digit number)

30696636304137910746…30790555126569728001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.139 × 10⁹⁷(98-digit number)

61393272608275821493…61581110253139456001

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