Block #298,006

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/7/2013, 12:43:38 AM · Difficulty 9.9919 · 6,492,936 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4edda2a8ceb583a4b18e3ec77de95dd143bc092d6675617836f338a505f76ee0

View on Chainz ↗

Height

#298,006

Difficulty

9.991948

Transactions

Size

358 B

Version

Bits

09fdf055

Nonce

141,032

Timestamp

12/7/2013, 12:43:38 AM

Confirmations

6,492,936

Merkle Root

e35f0a565a6c3cae4015bac8b6b16e70b01d39270d24c7862f9c364e005351b3

Transactions (2)

Coinbasea87165a1e879ef…880ca7e133fed4

1 in → 1 out10.0100 XPM110 B

AeKNrjNj…1NEq95Ta

8b576f96dff1cc…e3c9a8ab32f090

1 in → 1 out10.0800 XPM158 B

AXfJYKVn…QktpQC8p

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.

1.899 × 10⁹⁵(96-digit number)

18991578112746818071…33025888045223936001

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

1.899 × 10⁹⁵(96-digit number)

18991578112746818071…33025888045223936001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.798 × 10⁹⁵(96-digit number)

37983156225493636143…66051776090447872001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.596 × 10⁹⁵(96-digit number)

75966312450987272287…32103552180895744001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.519 × 10⁹⁶(97-digit number)

15193262490197454457…64207104361791488001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.038 × 10⁹⁶(97-digit number)

30386524980394908914…28414208723582976001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.077 × 10⁹⁶(97-digit number)

60773049960789817829…56828417447165952001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.215 × 10⁹⁷(98-digit number)

12154609992157963565…13656834894331904001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.430 × 10⁹⁷(98-digit number)

24309219984315927131…27313669788663808001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.861 × 10⁹⁷(98-digit number)

48618439968631854263…54627339577327616001

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