Block #204,492

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/11/2013, 1:04:10 PM · Difficulty 9.8986 · 6,595,750 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b14f764f8dd203e4cf740a79d051c270f9ed10f4603d3270f6296b6a911fc3aa

Height

#204,492

Difficulty

9.898634

Transactions

2

Size

4.69 KB

Version

2

Bits

09e60cde

Nonce

1,164,995,703

Timestamp

10/11/2013, 1:04:10 PM

Confirmations

6,595,750

Merkle Root

8e2ac6ff1aef23f8d574d098dd10010f86573f9b6e3442f02247895226ed8c27
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.

9.483 × 10⁹⁴(95-digit number)
94836401633758016525…84470022952144995841
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
9.483 × 10⁹⁴(95-digit number)
94836401633758016525…84470022952144995841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.896 × 10⁹⁵(96-digit number)
18967280326751603305…68940045904289991681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.793 × 10⁹⁵(96-digit number)
37934560653503206610…37880091808579983361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.586 × 10⁹⁵(96-digit number)
75869121307006413220…75760183617159966721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.517 × 10⁹⁶(97-digit number)
15173824261401282644…51520367234319933441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.034 × 10⁹⁶(97-digit number)
30347648522802565288…03040734468639866881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.069 × 10⁹⁶(97-digit number)
60695297045605130576…06081468937279733761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.213 × 10⁹⁷(98-digit number)
12139059409121026115…12162937874559467521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.427 × 10⁹⁷(98-digit number)
24278118818242052230…24325875749118935041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.855 × 10⁹⁷(98-digit number)
48556237636484104460…48651751498237870081
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:57,645,991 XPM·at block #6,800,241 · updates every 60s
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