Block #517,917

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/30/2014, 6:24:31 AM · Difficulty 10.8525 · 6,300,035 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7de35843cee584f22a12710c2860d187bb685615ffa15288653df74efebce719

Height

#517,917

Difficulty

10.852454

Transactions

3

Size

1.07 KB

Version

2

Bits

0ada3a68

Nonce

184,122,724

Timestamp

4/30/2014, 6:24:31 AM

Confirmations

6,300,035

Merkle Root

1463cc28e82e03b71f116e01de082c19fd09070f3b29679fbaff7c4a11e9a712
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.

2.143 × 10⁹¹(92-digit number)
21432529534306698890…60431801661115367501
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
2.143 × 10⁹¹(92-digit number)
21432529534306698890…60431801661115367501
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.286 × 10⁹¹(92-digit number)
42865059068613397781…20863603322230735001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.573 × 10⁹¹(92-digit number)
85730118137226795563…41727206644461470001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.714 × 10⁹²(93-digit number)
17146023627445359112…83454413288922940001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.429 × 10⁹²(93-digit number)
34292047254890718225…66908826577845880001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.858 × 10⁹²(93-digit number)
68584094509781436450…33817653155691760001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.371 × 10⁹³(94-digit number)
13716818901956287290…67635306311383520001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.743 × 10⁹³(94-digit number)
27433637803912574580…35270612622767040001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.486 × 10⁹³(94-digit number)
54867275607825149160…70541225245534080001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.097 × 10⁹⁴(95-digit number)
10973455121565029832…41082450491068160001
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:57,787,684 XPM·at block #6,817,951 · 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