Block #61,417

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 1:17:30 PM · Difficulty 8.9730 · 6,751,374 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

928a492d017bd062fd9b36b089bfe3568739a3e7b86a99a6e73438c662d33401

View on Chainz ↗

Height

#61,417

Difficulty

8.973021

Transactions

Size

199 B

Version

Bits

08f917e4

Nonce

205

Timestamp

7/18/2013, 1:17:30 PM

Confirmations

6,751,374

Mined by

⛏️ P2SHALXjrugCYbt29xU2ER2ywowb9GhByoynjy

Merkle Root

3921ed76a4461431d6e08a2ef3a3968da12718e9561a7acea4435a3808626691

Transactions (1)

Coinbase3921ed76a44614…435a3808626691

1 in → 1 out12.4000 XPM110 B

ALXjrugC…hByoynjy

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.

9.419 × 10⁹¹(92-digit number)

94190835695932222228…77949185966412779521

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

9.419 × 10⁹¹(92-digit number)

94190835695932222228…77949185966412779521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.883 × 10⁹²(93-digit number)

18838167139186444445…55898371932825559041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.767 × 10⁹²(93-digit number)

37676334278372888891…11796743865651118081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.535 × 10⁹²(93-digit number)

75352668556745777782…23593487731302236161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.507 × 10⁹³(94-digit number)

15070533711349155556…47186975462604472321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.014 × 10⁹³(94-digit number)

30141067422698311113…94373950925208944641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.028 × 10⁹³(94-digit number)

60282134845396622226…88747901850417889281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.205 × 10⁹⁴(95-digit number)

12056426969079324445…77495803700835778561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.411 × 10⁹⁴(95-digit number)

24112853938158648890…54991607401671557121

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 #61,417

Cookie Preferences