Block #203,999

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/11/2013, 5:36:18 AM · Difficulty 9.8977 · 6,622,656 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f586db7117d12f02fae869a5813c69223c7e5770d698b5b566210afef3e1cfe

Height

#203,999

Difficulty

9.897710

Transactions

4

Size

807 B

Version

2

Bits

09e5d050

Nonce

55,774

Timestamp

10/11/2013, 5:36:18 AM

Confirmations

6,622,656

Merkle Root

a38a2796b0ff0ef7845ed26c2d682367b3e67aafcf30deaed369338fbddb2746
Transactions (4)
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.

1.188 × 10⁹²(93-digit number)
11886143641040928985…05251370559908079241
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
1.188 × 10⁹²(93-digit number)
11886143641040928985…05251370559908079241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.377 × 10⁹²(93-digit number)
23772287282081857971…10502741119816158481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.754 × 10⁹²(93-digit number)
47544574564163715942…21005482239632316961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.508 × 10⁹²(93-digit number)
95089149128327431885…42010964479264633921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.901 × 10⁹³(94-digit number)
19017829825665486377…84021928958529267841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.803 × 10⁹³(94-digit number)
38035659651330972754…68043857917058535681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.607 × 10⁹³(94-digit number)
76071319302661945508…36087715834117071361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.521 × 10⁹⁴(95-digit number)
15214263860532389101…72175431668234142721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.042 × 10⁹⁴(95-digit number)
30428527721064778203…44350863336468285441
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,857,390 XPM·at block #6,826,654 · updates every 60s
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