Block #303,702

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/10/2013, 12:47:40 PM · Difficulty 9.9931 · 6,500,061 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2317921b3bb43aa4a31edfd154aa732061852e71778e9626b9eb536675339817

View on Chainz ↗

Height

#303,702

Difficulty

9.993094

Transactions

Size

1.08 KB

Version

Bits

09fe3b67

Nonce

16,533

Timestamp

12/10/2013, 12:47:40 PM

Confirmations

6,500,061

Mined by

⛏️ VaRAWXYBWKPhGt4UM6JfKUZgx3SbUqQAoisBJ

Merkle Root

e78d912c33e8c406836c57bc4cabb3837663304299057cdb0b84ee11023a13d4

Transactions (1)

Coinbasee78d912c33e8c4…84ee11023a13d4

1 in → 28 out9.9800 XPM1015 B

AWXYBWKP…qQAoisBJ AZ2pPuKg…95SN2Yr7 AG5YAjec…VhA4Aeh1 ASWX42VM…XypQABkY AQf7sjuh…sNY5fXpu

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.

5.491 × 10⁸⁹(90-digit number)

54914944978626883104…52311978324427344381

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

5.491 × 10⁸⁹(90-digit number)

54914944978626883104…52311978324427344381

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.098 × 10⁹⁰(91-digit number)

10982988995725376620…04623956648854688761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.196 × 10⁹⁰(91-digit number)

21965977991450753241…09247913297709377521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.393 × 10⁹⁰(91-digit number)

43931955982901506483…18495826595418755041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.786 × 10⁹⁰(91-digit number)

87863911965803012967…36991653190837510081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.757 × 10⁹¹(92-digit number)

17572782393160602593…73983306381675020161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.514 × 10⁹¹(92-digit number)

35145564786321205186…47966612763350040321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.029 × 10⁹¹(92-digit number)

70291129572642410373…95933225526700080641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.405 × 10⁹²(93-digit number)

14058225914528482074…91866451053400161281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.811 × 10⁹²(93-digit number)

28116451829056964149…83732902106800322561

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