Block #248,330

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/7/2013, 7:54:15 AM · Difficulty 9.9656 · 6,552,329 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2ffceac13cfb5e880ec8f811e8e42c1a319bc9fcf07360eedd8c61e90c65562e

View on Chainz ↗

Height

#248,330

Difficulty

9.965582

Transactions

Size

1.97 KB

Version

Bits

09f7305f

Nonce

168,397

Timestamp

11/7/2013, 7:54:15 AM

Confirmations

6,552,329

Mined by

⛏️ R{G+AHxLfgpF3Ahonu63kdKbiGfoomaHZFyT2s

Merkle Root

ba702ea48f6976cf573e20add2cb29c9f8b0495f0c29889bd4c6fea59bd597ab

Transactions (1)

Coinbaseba702ea48f6976…c6fea59bd597ab

1 in → 55 out10.0300 XPM1.89 KB

AHxLfgpF…aHZFyT2s ARpndEmc…Hg792kEk ANsrD1P6…m3RxY4uj AG9H2B8p…eiaSPdGS AKDTDDtx…iqvw9cdY

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.

5.920 × 10⁹¹(92-digit number)

59203957387725290730…85952177565850137921

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

5.920 × 10⁹¹(92-digit number)

59203957387725290730…85952177565850137921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.184 × 10⁹²(93-digit number)

11840791477545058146…71904355131700275841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.368 × 10⁹²(93-digit number)

23681582955090116292…43808710263400551681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.736 × 10⁹²(93-digit number)

47363165910180232584…87617420526801103361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.472 × 10⁹²(93-digit number)

94726331820360465168…75234841053602206721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.894 × 10⁹³(94-digit number)

18945266364072093033…50469682107204413441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.789 × 10⁹³(94-digit number)

37890532728144186067…00939364214408826881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.578 × 10⁹³(94-digit number)

75781065456288372134…01878728428817653761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.515 × 10⁹⁴(95-digit number)

15156213091257674426…03757456857635307521

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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