Block #1,886,019

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/9/2016, 11:17:18 AM · Difficulty 10.7205 · 4,944,835 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5b93dde26931b8d1c09ef4f7130aab3f68f0ed839e490dd0c4866efabe525f26

Height

#1,886,019

Difficulty

10.720501

Transactions

2

Size

1016 B

Version

2

Bits

0ab872c1

Nonce

84,899,531

Timestamp

12/9/2016, 11:17:18 AM

Confirmations

4,944,835

Merkle Root

8446448ec08951aa3816af00acfecc5fba82a8c16ea9b1c15946ebd3110c3a6c
Transactions (2)
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.

5.098 × 10⁹¹(92-digit number)
50984663401993785214…21711848639260126201
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
5.098 × 10⁹¹(92-digit number)
50984663401993785214…21711848639260126201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.019 × 10⁹²(93-digit number)
10196932680398757042…43423697278520252401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.039 × 10⁹²(93-digit number)
20393865360797514085…86847394557040504801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.078 × 10⁹²(93-digit number)
40787730721595028171…73694789114081009601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.157 × 10⁹²(93-digit number)
81575461443190056342…47389578228162019201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.631 × 10⁹³(94-digit number)
16315092288638011268…94779156456324038401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.263 × 10⁹³(94-digit number)
32630184577276022536…89558312912648076801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.526 × 10⁹³(94-digit number)
65260369154552045073…79116625825296153601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.305 × 10⁹⁴(95-digit number)
13052073830910409014…58233251650592307201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.610 × 10⁹⁴(95-digit number)
26104147661820818029…16466503301184614401
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:57,890,968 XPM·at block #6,830,853 · updates every 60s
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