Block #244,460

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/4/2013, 9:17:04 PM · Difficulty 9.9629 · 6,562,989 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
95f9cf9ce774aae78cfb26196abc7a1b53e4c7ec4573b40e8f8a6572647ff64c

Height

#244,460

Difficulty

9.962924

Transactions

2

Size

752 B

Version

2

Bits

09f68231

Nonce

18,928

Timestamp

11/4/2013, 9:17:04 PM

Confirmations

6,562,989

Merkle Root

039235ebc4d458fa87f28d819b3e3e0fd2751ee6d521e32f8c1734b69a7101c0
Transactions (2)
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.

1.066 × 10⁹⁹(100-digit number)
10667899439591911106…04087000799775251201
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
1.066 × 10⁹⁹(100-digit number)
10667899439591911106…04087000799775251201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.133 × 10⁹⁹(100-digit number)
21335798879183822213…08174001599550502401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.267 × 10⁹⁹(100-digit number)
42671597758367644426…16348003199101004801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.534 × 10⁹⁹(100-digit number)
85343195516735288852…32696006398202009601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.706 × 10¹⁰⁰(101-digit number)
17068639103347057770…65392012796404019201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.413 × 10¹⁰⁰(101-digit number)
34137278206694115540…30784025592808038401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.827 × 10¹⁰⁰(101-digit number)
68274556413388231081…61568051185616076801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.365 × 10¹⁰¹(102-digit number)
13654911282677646216…23136102371232153601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.730 × 10¹⁰¹(102-digit number)
27309822565355292432…46272204742464307201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.461 × 10¹⁰¹(102-digit number)
54619645130710584865…92544409484928614401
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:57,703,614 XPM·at block #6,807,448 · updates every 60s
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