Block #2,676,543

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/24/2018, 10:57:29 PM · Difficulty 11.6976 · 4,154,902 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2390c74e75436964f5db942dea213bfc92253986ae6a4909916b1cc2838d1733

Height

#2,676,543

Difficulty

11.697597

Transactions

4

Size

1.48 KB

Version

2

Bits

0bb295b4

Nonce

162,954,639

Timestamp

5/24/2018, 10:57:29 PM

Confirmations

4,154,902

Merkle Root

e87e48a7a4751134acac651cc8d253c6a9ccf03077ca2e078b129c8974818289
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.

5.016 × 10⁹⁶(97-digit number)
50167126017077614968…03771962610570432001
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
5.016 × 10⁹⁶(97-digit number)
50167126017077614968…03771962610570432001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.003 × 10⁹⁷(98-digit number)
10033425203415522993…07543925221140864001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.006 × 10⁹⁷(98-digit number)
20066850406831045987…15087850442281728001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.013 × 10⁹⁷(98-digit number)
40133700813662091975…30175700884563456001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.026 × 10⁹⁷(98-digit number)
80267401627324183950…60351401769126912001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.605 × 10⁹⁸(99-digit number)
16053480325464836790…20702803538253824001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.210 × 10⁹⁸(99-digit number)
32106960650929673580…41405607076507648001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.421 × 10⁹⁸(99-digit number)
64213921301859347160…82811214153015296001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.284 × 10⁹⁹(100-digit number)
12842784260371869432…65622428306030592001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.568 × 10⁹⁹(100-digit number)
25685568520743738864…31244856612061184001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.137 × 10⁹⁹(100-digit number)
51371137041487477728…62489713224122368001
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:57,895,724 XPM·at block #6,831,444 · updates every 60s
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