Block #201,454

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/9/2013, 3:55:39 PM · Difficulty 9.8916 · 6,600,186 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
42e18dd3b457ae72318cd439e3d7b514e3c0f44c5b2ab20ac6fe4a3e75db226b

Height

#201,454

Difficulty

9.891566

Transactions

1

Size

4.17 KB

Version

2

Bits

09e43da3

Nonce

1,164,739,872

Timestamp

10/9/2013, 3:55:39 PM

Confirmations

6,600,186

Merkle Root

4b0159c4e522391acb287cdd355b01b24b7db32794678de86927aad0d310d3c5
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.

3.066 × 10⁹³(94-digit number)
30660661323719801706…75757449839064787199
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
3.066 × 10⁹³(94-digit number)
30660661323719801706…75757449839064787199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.132 × 10⁹³(94-digit number)
61321322647439603412…51514899678129574399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.226 × 10⁹⁴(95-digit number)
12264264529487920682…03029799356259148799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.452 × 10⁹⁴(95-digit number)
24528529058975841365…06059598712518297599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.905 × 10⁹⁴(95-digit number)
49057058117951682730…12119197425036595199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.811 × 10⁹⁴(95-digit number)
98114116235903365460…24238394850073190399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.962 × 10⁹⁵(96-digit number)
19622823247180673092…48476789700146380799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.924 × 10⁹⁵(96-digit number)
39245646494361346184…96953579400292761599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.849 × 10⁹⁵(96-digit number)
78491292988722692368…93907158800585523199
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,657,200 XPM·at block #6,801,639 · updates every 60s
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