Block #911,578

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2015, 5:21:59 AM · Difficulty 10.9308 · 5,913,915 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
51379512c4b6549821ddc35c0edc5bb9e213a9a385e5f53c21a4f17fdf6d1320

Height

#911,578

Difficulty

10.930844

Transactions

6

Size

2.17 KB

Version

2

Bits

0aee4bd1

Nonce

696,211,528

Timestamp

1/27/2015, 5:21:59 AM

Confirmations

5,913,915

Merkle Root

95c2131d04e81308171c04b89815088ead8dfb011d645290b1f2ada4d33cb793
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.

1.368 × 10⁹⁵(96-digit number)
13687831494577430909…44607540941043658881
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
1.368 × 10⁹⁵(96-digit number)
13687831494577430909…44607540941043658881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.737 × 10⁹⁵(96-digit number)
27375662989154861819…89215081882087317761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.475 × 10⁹⁵(96-digit number)
54751325978309723639…78430163764174635521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.095 × 10⁹⁶(97-digit number)
10950265195661944727…56860327528349271041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.190 × 10⁹⁶(97-digit number)
21900530391323889455…13720655056698542081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.380 × 10⁹⁶(97-digit number)
43801060782647778911…27441310113397084161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.760 × 10⁹⁶(97-digit number)
87602121565295557823…54882620226794168321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.752 × 10⁹⁷(98-digit number)
17520424313059111564…09765240453588336641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.504 × 10⁹⁷(98-digit number)
35040848626118223129…19530480907176673281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.008 × 10⁹⁷(98-digit number)
70081697252236446258…39060961814353346561
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:57,848,039 XPM·at block #6,825,492 · 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