Block #2,455,147

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/3/2018, 4:20:36 AM · Difficulty 10.9524 · 4,384,460 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bfbbabe9d2cd14d9b3ff8ca3cb4c5361f467b8ce13f189cc80cef312a2817231

Height

#2,455,147

Difficulty

10.952418

Transactions

15

Size

4.29 KB

Version

2

Bits

0af3d1b1

Nonce

1,902,391,920

Timestamp

1/3/2018, 4:20:36 AM

Confirmations

4,384,460

Merkle Root

33023528c4bbde5290caf0e6891f3c3eb5702497948df6cce68380f9ea1b3a64
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.

1.340 × 10⁹⁵(96-digit number)
13407504118725941529…35379421715793667201
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
1.340 × 10⁹⁵(96-digit number)
13407504118725941529…35379421715793667201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.681 × 10⁹⁵(96-digit number)
26815008237451883058…70758843431587334401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.363 × 10⁹⁵(96-digit number)
53630016474903766117…41517686863174668801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.072 × 10⁹⁶(97-digit number)
10726003294980753223…83035373726349337601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.145 × 10⁹⁶(97-digit number)
21452006589961506446…66070747452698675201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.290 × 10⁹⁶(97-digit number)
42904013179923012893…32141494905397350401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.580 × 10⁹⁶(97-digit number)
85808026359846025787…64282989810794700801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.716 × 10⁹⁷(98-digit number)
17161605271969205157…28565979621589401601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.432 × 10⁹⁷(98-digit number)
34323210543938410314…57131959243178803201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.864 × 10⁹⁷(98-digit number)
68646421087876820629…14263918486357606401
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:57,961,145 XPM·at block #6,839,606 · 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