Block #2,844,602

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/18/2018, 8:29:35 AM · Difficulty 11.7281 · 3,986,840 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
54b49f5d59f3d745a6f222358a7bba37d9ac90e320dfacdd4db8dfadb48bbbaa

Height

#2,844,602

Difficulty

11.728052

Transactions

4

Size

1.22 KB

Version

2

Bits

0bba61a3

Nonce

170,881,551

Timestamp

9/18/2018, 8:29:35 AM

Confirmations

3,986,840

Merkle Root

0d823967043e812f5a955f873eeca8d6961c15503800ef6eb79a76e0f93794bb
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.

2.418 × 10⁹¹(92-digit number)
24183638767211031169…41731066014240109861
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
2.418 × 10⁹¹(92-digit number)
24183638767211031169…41731066014240109861
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.836 × 10⁹¹(92-digit number)
48367277534422062338…83462132028480219721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.673 × 10⁹¹(92-digit number)
96734555068844124677…66924264056960439441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.934 × 10⁹²(93-digit number)
19346911013768824935…33848528113920878881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.869 × 10⁹²(93-digit number)
38693822027537649870…67697056227841757761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.738 × 10⁹²(93-digit number)
77387644055075299741…35394112455683515521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.547 × 10⁹³(94-digit number)
15477528811015059948…70788224911367031041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.095 × 10⁹³(94-digit number)
30955057622030119896…41576449822734062081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.191 × 10⁹³(94-digit number)
61910115244060239793…83152899645468124161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.238 × 10⁹⁴(95-digit number)
12382023048812047958…66305799290936248321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.476 × 10⁹⁴(95-digit number)
24764046097624095917…32611598581872496641
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,895,700 XPM·at block #6,831,441 · 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