Block #335,745

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/30/2013, 11:22:50 AM · Difficulty 10.1452 · 6,467,734 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

72ed6834aa5e9bf08469ec49cc61bef7feea5501873d7bdcc9debc408c31041e

View on Chainz ↗

Height

#335,745

Difficulty

10.145217

Transactions

Size

1.08 KB

Version

Bits

0a252cf2

Nonce

32,877

Timestamp

12/30/2013, 11:22:50 AM

Confirmations

6,467,734

Mined by

⛏️ aRW\AQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

0ae790e3fafc221d991e7ff67a53b6f0b683f6c30083353888cc54e979e3b173

Transactions (1)

Coinbase0ae790e3fafc22…cc54e979e3b173

1 in → 28 out9.6800 XPM1015 B

AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 Ad9pSzHt…cpJ3y2zz AXeQnyEs…fUWKQwq8

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.

6.291 × 10⁹²(93-digit number)

62914354163288146666…86977055684899048961

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

6.291 × 10⁹²(93-digit number)

62914354163288146666…86977055684899048961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.258 × 10⁹³(94-digit number)

12582870832657629333…73954111369798097921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.516 × 10⁹³(94-digit number)

25165741665315258666…47908222739596195841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.033 × 10⁹³(94-digit number)

50331483330630517333…95816445479192391681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.006 × 10⁹⁴(95-digit number)

10066296666126103466…91632890958384783361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.013 × 10⁹⁴(95-digit number)

20132593332252206933…83265781916769566721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.026 × 10⁹⁴(95-digit number)

40265186664504413866…66531563833539133441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.053 × 10⁹⁴(95-digit number)

80530373329008827732…33063127667078266881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.610 × 10⁹⁵(96-digit number)

16106074665801765546…66126255334156533761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.221 × 10⁹⁵(96-digit number)

32212149331603531093…32252510668313067521

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