Block #310,778

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/14/2013, 5:57:26 AM · Difficulty 9.9953 · 6,488,577 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a32f8f38ffd273185f202fa5a8285dd996bff35459f5d118d91a63ea0f4cbd51

View on Chainz ↗

Height

#310,778

Difficulty

9.995284

Transactions

Size

1.11 KB

Version

Bits

09fecaea

Nonce

7,843

Timestamp

12/14/2013, 5:57:26 AM

Confirmations

6,488,577

Mined by

⛏️ aR'Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

fe076056028fcbae3d909d2f98c326a6acff00f9151a8462fa7b6ecf712b6e27

Transactions (1)

Coinbasefe076056028fcb…7b6ecf712b6e27

1 in → 29 out9.9700 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz AYcLTeXR…bscgPops Aac9Hjdg…P4ktypc3 AcM3ext6…Hwtj9Qp3 ASFLBMf4…aN3am9vA

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.

8.708 × 10⁹⁷(98-digit number)

87089259019749670536…40892568488578246241

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

8.708 × 10⁹⁷(98-digit number)

87089259019749670536…40892568488578246241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.741 × 10⁹⁸(99-digit number)

17417851803949934107…81785136977156492481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.483 × 10⁹⁸(99-digit number)

34835703607899868214…63570273954312984961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.967 × 10⁹⁸(99-digit number)

69671407215799736428…27140547908625969921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.393 × 10⁹⁹(100-digit number)

13934281443159947285…54281095817251939841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.786 × 10⁹⁹(100-digit number)

27868562886319894571…08562191634503879681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.573 × 10⁹⁹(100-digit number)

55737125772639789143…17124383269007759361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.114 × 10¹⁰⁰(101-digit number)

11147425154527957828…34248766538015518721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.229 × 10¹⁰⁰(101-digit number)

22294850309055915657…68497533076031037441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.458 × 10¹⁰⁰(101-digit number)

44589700618111831314…36995066152062074881

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