Block #305,207

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2013, 8:40:36 AM · Difficulty 9.9935 · 6,497,813 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a348c5a8d03764f0197ea0c5c907870f45001ee230b4279b81469fbebb0296f8

View on Chainz ↗

Height

#305,207

Difficulty

9.993537

Transactions

Size

1.01 KB

Version

Bits

09fe5877

Nonce

13,074

Timestamp

12/11/2013, 8:40:36 AM

Confirmations

6,497,813

Mined by

⛏️ 7aR'AHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

ab44e9cc5fa834fb3555bc150c25fd115e74fe303bf679a57b2e0be15c5ea89d

Transactions (1)

Coinbaseab44e9cc5fa834…2e0be15c5ea89d

1 in → 26 out10.0000 XPM947 B

AHuJ9wYh…BGmgHrKZ AcC2zSod…rtWatH79 Ad9pSzHt…cpJ3y2zz AG5YAjec…VhA4Aeh1 AMzKpXdM…uGc2qtna

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.

7.754 × 10⁹⁸(99-digit number)

77545541550365331629…62982664889152627201

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

7.754 × 10⁹⁸(99-digit number)

77545541550365331629…62982664889152627201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.550 × 10⁹⁹(100-digit number)

15509108310073066325…25965329778305254401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.101 × 10⁹⁹(100-digit number)

31018216620146132651…51930659556610508801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.203 × 10⁹⁹(100-digit number)

62036433240292265303…03861319113221017601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.240 × 10¹⁰⁰(101-digit number)

12407286648058453060…07722638226442035201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.481 × 10¹⁰⁰(101-digit number)

24814573296116906121…15445276452884070401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.962 × 10¹⁰⁰(101-digit number)

49629146592233812242…30890552905768140801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.925 × 10¹⁰⁰(101-digit number)

99258293184467624485…61781105811536281601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.985 × 10¹⁰¹(102-digit number)

19851658636893524897…23562211623072563201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.970 × 10¹⁰¹(102-digit number)

39703317273787049794…47124423246145126401

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