Block #92,025

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/1/2013, 9:41:53 AM · Difficulty 9.2081 · 6,724,868 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cbeec0df026a10b177133b13e70d100f35489ee589a4382ac41196cc8e5fbfa7

Height

#92,025

Difficulty

9.208106

Transactions

4

Size

1.16 KB

Version

2

Bits

09354675

Nonce

441,147

Timestamp

8/1/2013, 9:41:53 AM

Confirmations

6,724,868

Merkle Root

fb5df668308af46a4350a0142692f6eff80b8b906eae212eeb4c4aa3d051741f
Transactions (4)
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.

1.135 × 10⁹⁷(98-digit number)
11355486168306090449…66946014312609056421
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
1.135 × 10⁹⁷(98-digit number)
11355486168306090449…66946014312609056421
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.271 × 10⁹⁷(98-digit number)
22710972336612180898…33892028625218112841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.542 × 10⁹⁷(98-digit number)
45421944673224361797…67784057250436225681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.084 × 10⁹⁷(98-digit number)
90843889346448723594…35568114500872451361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.816 × 10⁹⁸(99-digit number)
18168777869289744718…71136229001744902721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.633 × 10⁹⁸(99-digit number)
36337555738579489437…42272458003489805441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.267 × 10⁹⁸(99-digit number)
72675111477158978875…84544916006979610881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.453 × 10⁹⁹(100-digit number)
14535022295431795775…69089832013959221761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.907 × 10⁹⁹(100-digit number)
29070044590863591550…38179664027918443521
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:57,779,185 XPM·at block #6,816,892 · 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