Block #302,348

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/9/2013, 6:34:01 PM · Difficulty 9.9927 · 6,505,538 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

02e184ad71d2bf995eda9e5f44dd64d4d3c8c20c849f921287657638544714d6

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Height

#302,348

Difficulty

9.992683

Transactions

Size

1.14 KB

Version

Bits

09fe207f

Nonce

147,943

Timestamp

12/9/2013, 6:34:01 PM

Confirmations

6,505,538

Mined by

⛏️ aRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

24c5a68c10ca8b4e097a7cba68fbd52601f11333f175b79ed46cdae65d903ac8

Transactions (1)

Coinbase24c5a68c10ca8b…6cdae65d903ac8

1 in → 30 out9.9800 XPM1.06 KB

Ad9pSzHt…cpJ3y2zz AYtDvcGs…VuAcA7m7 AHuJ9wYh…BGmgHrKZ AMPANLy7…kkN5vWzv ATZCZabL…FHs8ADLe

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.

6.272 × 10⁹²(93-digit number)

62725259669541200638…62621422031895422721

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

6.272 × 10⁹²(93-digit number)

62725259669541200638…62621422031895422721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.254 × 10⁹³(94-digit number)

12545051933908240127…25242844063790845441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.509 × 10⁹³(94-digit number)

25090103867816480255…50485688127581690881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.018 × 10⁹³(94-digit number)

50180207735632960510…00971376255163381761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.003 × 10⁹⁴(95-digit number)

10036041547126592102…01942752510326763521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.007 × 10⁹⁴(95-digit number)

20072083094253184204…03885505020653527041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.014 × 10⁹⁴(95-digit number)

40144166188506368408…07771010041307054081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.028 × 10⁹⁴(95-digit number)

80288332377012736817…15542020082614108161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.605 × 10⁹⁵(96-digit number)

16057666475402547363…31084040165228216321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.211 × 10⁹⁵(96-digit number)

32115332950805094726…62168080330456432641

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 #302,348

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