Block #244,483

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/4/2013, 9:37:59 PM · Difficulty 9.9629 · 6,580,298 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
00f03b706bdb4fc18624a9f4f7aa46de536fc35961a4389fb35eb4dc1bb62356

Height

#244,483

Difficulty

9.962940

Transactions

3

Size

650 B

Version

2

Bits

09f68336

Nonce

24,218

Timestamp

11/4/2013, 9:37:59 PM

Confirmations

6,580,298

Merkle Root

3b4d332dc73130273700062355d768646442e5d6c947f94be5b991fc4ed2cd51
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.

1.463 × 10⁹⁰(91-digit number)
14631483696533669025…34236989622113971001
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.

1
origin + 1
1.463 × 10⁹⁰(91-digit number)
14631483696533669025…34236989622113971001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.926 × 10⁹⁰(91-digit number)
29262967393067338050…68473979244227942001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.852 × 10⁹⁰(91-digit number)
58525934786134676100…36947958488455884001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.170 × 10⁹¹(92-digit number)
11705186957226935220…73895916976911768001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.341 × 10⁹¹(92-digit number)
23410373914453870440…47791833953823536001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.682 × 10⁹¹(92-digit number)
46820747828907740880…95583667907647072001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.364 × 10⁹¹(92-digit number)
93641495657815481760…91167335815294144001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.872 × 10⁹²(93-digit number)
18728299131563096352…82334671630588288001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.745 × 10⁹²(93-digit number)
37456598263126192704…64669343261176576001
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, …
Circulating Supply:57,842,321 XPM·at block #6,824,780 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy