Block #396,201

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/9/2014, 6:29:37 AM · Difficulty 10.4094 · 6,410,300 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
982adc457817cc3e3c1b82f73b0e9155832b6c06c7a4a09dbc7b8e542137455e

Height

#396,201

Difficulty

10.409399

Transactions

1

Size

902 B

Version

2

Bits

0a68ce64

Nonce

87,145

Timestamp

2/9/2014, 6:29:37 AM

Confirmations

6,410,300

Merkle Root

4121c57a331f025085ae5191cfa5105731a0c3a1e97ccb80458522f3628d6b4c
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.

4.454 × 10⁹⁷(98-digit number)
44549395097651164081…57251299476891095101
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
4.454 × 10⁹⁷(98-digit number)
44549395097651164081…57251299476891095101
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.909 × 10⁹⁷(98-digit number)
89098790195302328162…14502598953782190201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.781 × 10⁹⁸(99-digit number)
17819758039060465632…29005197907564380401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.563 × 10⁹⁸(99-digit number)
35639516078120931264…58010395815128760801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.127 × 10⁹⁸(99-digit number)
71279032156241862529…16020791630257521601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.425 × 10⁹⁹(100-digit number)
14255806431248372505…32041583260515043201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.851 × 10⁹⁹(100-digit number)
28511612862496745011…64083166521030086401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.702 × 10⁹⁹(100-digit number)
57023225724993490023…28166333042060172801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.140 × 10¹⁰⁰(101-digit number)
11404645144998698004…56332666084120345601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.280 × 10¹⁰⁰(101-digit number)
22809290289997396009…12665332168240691201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.561 × 10¹⁰⁰(101-digit number)
45618580579994792019…25330664336481382401
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:57,696,104 XPM·at block #6,806,500 · 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.

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