Block #278,069

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/27/2013, 8:16:20 PM · Difficulty 9.9679 · 6,532,918 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

01c44cf46e7769bc7a970978df7b849a9f449dbab076e6803cab8f5cc65c4903

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Height

#278,069

Difficulty

9.967931

Transactions

Size

1.11 KB

Version

Bits

09f7ca52

Nonce

3,069

Timestamp

11/27/2013, 8:16:20 PM

Confirmations

6,532,918

Mined by

⛏️ 5>aRSAbtgNzNbw1hJh3uoaBwXxdpmiY9Atvu81w

Merkle Root

3f3fe010584a829a1c88ba8504d495806c2b809236b2b2de43535f8681c15b98

Transactions (1)

Coinbase3f3fe010584a82…535f8681c15b98

1 in → 29 out10.0300 XPM1.02 KB

AbtgNzNb…9Atvu81w Ad9pSzHt…cpJ3y2zz AUSdJaEr…Y4n4oUzF AMbCuLHZ…WSoStwkc AYrgZtF4…6oLCC7XK

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.

3.798 × 10⁹³(94-digit number)

37986056800898004775…51097437905285138941

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

3.798 × 10⁹³(94-digit number)

37986056800898004775…51097437905285138941

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.597 × 10⁹³(94-digit number)

75972113601796009550…02194875810570277881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.519 × 10⁹⁴(95-digit number)

15194422720359201910…04389751621140555761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.038 × 10⁹⁴(95-digit number)

30388845440718403820…08779503242281111521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.077 × 10⁹⁴(95-digit number)

60777690881436807640…17559006484562223041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.215 × 10⁹⁵(96-digit number)

12155538176287361528…35118012969124446081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.431 × 10⁹⁵(96-digit number)

24311076352574723056…70236025938248892161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.862 × 10⁹⁵(96-digit number)

48622152705149446112…40472051876497784321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.724 × 10⁹⁵(96-digit number)

97244305410298892224…80944103752995568641

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

Block #278,069

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