Block #206,448

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/12/2013, 7:42:32 PM · Difficulty 9.9011 · 6,603,956 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e3ecae8e1aa0893c72336e33b2d19c6db7750cae22725285fbcd5458ee088e53

Height

#206,448

Difficulty

9.901087

Transactions

1

Size

198 B

Version

2

Bits

09e6ad9c

Nonce

14,312

Timestamp

10/12/2013, 7:42:32 PM

Confirmations

6,603,956

Merkle Root

2792129f6721032be955eeae2421ba384527c1b8904788722d15e8c620e05f9e
Transactions (1)
1 in → 1 out10.1900 XPM109 B
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.

1.232 × 10⁹¹(92-digit number)
12329778748571050967…35032190515042600251
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
1.232 × 10⁹¹(92-digit number)
12329778748571050967…35032190515042600251
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.465 × 10⁹¹(92-digit number)
24659557497142101934…70064381030085200501
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.931 × 10⁹¹(92-digit number)
49319114994284203868…40128762060170401001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.863 × 10⁹¹(92-digit number)
98638229988568407737…80257524120340802001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.972 × 10⁹²(93-digit number)
19727645997713681547…60515048240681604001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.945 × 10⁹²(93-digit number)
39455291995427363094…21030096481363208001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.891 × 10⁹²(93-digit number)
78910583990854726189…42060192962726416001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.578 × 10⁹³(94-digit number)
15782116798170945237…84120385925452832001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.156 × 10⁹³(94-digit number)
31564233596341890475…68240771850905664001
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:57,727,310 XPM·at block #6,810,403 · 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