Block #227,860

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/26/2013, 3:44:15 AM · Difficulty 9.9371 · 6,598,539 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2d3c69c4ac223f4f03a662ed6b1a83af3cad8bc0ab66f527e9486f58c2ea13d5

Height

#227,860

Difficulty

9.937145

Transactions

4

Size

843 B

Version

2

Bits

09efe8c2

Nonce

96,222

Timestamp

10/26/2013, 3:44:15 AM

Confirmations

6,598,539

Merkle Root

ddce1b30da964d1f2e7f4eccf8280851a00f519850537687113b077647398778
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.

2.799 × 10⁹¹(92-digit number)
27995365754992747131…85021585437718286621
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
2.799 × 10⁹¹(92-digit number)
27995365754992747131…85021585437718286621
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.599 × 10⁹¹(92-digit number)
55990731509985494263…70043170875436573241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.119 × 10⁹²(93-digit number)
11198146301997098852…40086341750873146481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.239 × 10⁹²(93-digit number)
22396292603994197705…80172683501746292961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.479 × 10⁹²(93-digit number)
44792585207988395411…60345367003492585921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.958 × 10⁹²(93-digit number)
89585170415976790822…20690734006985171841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.791 × 10⁹³(94-digit number)
17917034083195358164…41381468013970343681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.583 × 10⁹³(94-digit number)
35834068166390716328…82762936027940687361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.166 × 10⁹³(94-digit number)
71668136332781432657…65525872055881374721
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:57,855,332 XPM·at block #6,826,398 · updates every 60s
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