Block #1,368,049

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/13/2015, 2:06:32 PM · Difficulty 10.8387 · 5,458,941 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7faeebdad5670bcbd71b51efbd9d7903aba857d90a95175b47177308f47d4ba7

Height

#1,368,049

Difficulty

10.838676

Transactions

2

Size

867 B

Version

2

Bits

0ad6b377

Nonce

815,673,199

Timestamp

12/13/2015, 2:06:32 PM

Confirmations

5,458,941

Merkle Root

6360ed49549f1796510ccb95c47e91d39fe6b425e574ed379e6a2a439614cd20
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.

3.917 × 10⁹⁴(95-digit number)
39172477391466795159…38276392146228425601
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
3.917 × 10⁹⁴(95-digit number)
39172477391466795159…38276392146228425601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.834 × 10⁹⁴(95-digit number)
78344954782933590318…76552784292456851201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.566 × 10⁹⁵(96-digit number)
15668990956586718063…53105568584913702401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.133 × 10⁹⁵(96-digit number)
31337981913173436127…06211137169827404801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.267 × 10⁹⁵(96-digit number)
62675963826346872254…12422274339654809601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.253 × 10⁹⁶(97-digit number)
12535192765269374450…24844548679309619201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.507 × 10⁹⁶(97-digit number)
25070385530538748901…49689097358619238401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.014 × 10⁹⁶(97-digit number)
50140771061077497803…99378194717238476801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.002 × 10⁹⁷(98-digit number)
10028154212215499560…98756389434476953601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.005 × 10⁹⁷(98-digit number)
20056308424430999121…97512778868953907201
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,860,094 XPM·at block #6,826,989 · 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