Block #532,092

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/8/2014, 9:44:17 PM · Difficulty 10.8960 · 6,270,150 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a2f2dbc83cc81093bb8085e7cbdeda511f3953804abe493b8a7b82b38cc5e62f

Height

#532,092

Difficulty

10.895999

Transactions

5

Size

1.81 KB

Version

2

Bits

0ae56037

Nonce

17,394,352

Timestamp

5/8/2014, 9:44:17 PM

Confirmations

6,270,150

Merkle Root

1adcdfe9beefa561f74b6da9e4628244007795582f0369beea838c83565444f1
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.

4.267 × 10⁹⁹(100-digit number)
42670417891679815832…75861917094357670401
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
4.267 × 10⁹⁹(100-digit number)
42670417891679815832…75861917094357670401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.534 × 10⁹⁹(100-digit number)
85340835783359631664…51723834188715340801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.706 × 10¹⁰⁰(101-digit number)
17068167156671926332…03447668377430681601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.413 × 10¹⁰⁰(101-digit number)
34136334313343852665…06895336754861363201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.827 × 10¹⁰⁰(101-digit number)
68272668626687705331…13790673509722726401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.365 × 10¹⁰¹(102-digit number)
13654533725337541066…27581347019445452801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.730 × 10¹⁰¹(102-digit number)
27309067450675082132…55162694038890905601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.461 × 10¹⁰¹(102-digit number)
54618134901350164265…10325388077781811201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.092 × 10¹⁰²(103-digit number)
10923626980270032853…20650776155563622401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.184 × 10¹⁰²(103-digit number)
21847253960540065706…41301552311127244801
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:57,661,945 XPM·at block #6,802,241 · updates every 60s
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