Block #2,646,829

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/3/2018, 1:46:57 PM · Difficulty 11.7550 · 4,196,385 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dc428a9221d64cfcd7dfbee3274f772aa61a086ebf92477bbffaa743467fa33b

Height

#2,646,829

Difficulty

11.754960

Transactions

5

Size

1.51 KB

Version

2

Bits

0bc14514

Nonce

341,740,888

Timestamp

5/3/2018, 1:46:57 PM

Confirmations

4,196,385

Merkle Root

b9f7e1e6befaf03a0bad18444f7e5289990060ededd5b90c72418e224fcafd88
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.

5.832 × 10⁹³(94-digit number)
58325945461616231218…11897149134664504081
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
5.832 × 10⁹³(94-digit number)
58325945461616231218…11897149134664504081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.166 × 10⁹⁴(95-digit number)
11665189092323246243…23794298269329008161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.333 × 10⁹⁴(95-digit number)
23330378184646492487…47588596538658016321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.666 × 10⁹⁴(95-digit number)
46660756369292984975…95177193077316032641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.332 × 10⁹⁴(95-digit number)
93321512738585969950…90354386154632065281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.866 × 10⁹⁵(96-digit number)
18664302547717193990…80708772309264130561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.732 × 10⁹⁵(96-digit number)
37328605095434387980…61417544618528261121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.465 × 10⁹⁵(96-digit number)
74657210190868775960…22835089237056522241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.493 × 10⁹⁶(97-digit number)
14931442038173755192…45670178474113044481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.986 × 10⁹⁶(97-digit number)
29862884076347510384…91340356948226088961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.972 × 10⁹⁶(97-digit number)
59725768152695020768…82680713896452177921
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,990,085 XPM·at block #6,843,213 · 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