Block #310,264

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/13/2013, 11:54:48 PM · Difficulty 9.9951 · 6,515,048 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7842a5e4002c7f1b97fe61fb52903a514071eeea9fab3f0ff24a8560773b6787

View on Chainz ↗

Height

#310,264

Difficulty

9.995124

Transactions

Size

212 B

Version

Bits

09fec06f

Nonce

342

Timestamp

12/13/2013, 11:54:48 PM

Confirmations

6,515,048

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6d6fda44a1d8c24a63822222d9ab50a0e817a34fa051e9ab63d1114b1c1e014f

Transactions (1)

Coinbase6d6fda44a1d8c2…d1114b1c1e014f

1 in → 1 out9.9900 XPM116 B

AbwWkWZt…kawDhufa

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.

2.495 × 10¹⁰⁸(109-digit number)

24952132246665676823…28111752756943912961

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

2.495 × 10¹⁰⁸(109-digit number)

24952132246665676823…28111752756943912961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.990 × 10¹⁰⁸(109-digit number)

49904264493331353646…56223505513887825921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.980 × 10¹⁰⁸(109-digit number)

99808528986662707292…12447011027775651841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.996 × 10¹⁰⁹(110-digit number)

19961705797332541458…24894022055551303681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.992 × 10¹⁰⁹(110-digit number)

39923411594665082916…49788044111102607361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.984 × 10¹⁰⁹(110-digit number)

79846823189330165833…99576088222205214721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.596 × 10¹¹⁰(111-digit number)

15969364637866033166…99152176444410429441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.193 × 10¹¹⁰(111-digit number)

31938729275732066333…98304352888820858881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.387 × 10¹¹⁰(111-digit number)

63877458551464132667…96608705777641717761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.277 × 10¹¹¹(112-digit number)

12775491710292826533…93217411555283435521

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

Block #310,264

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