Block #487,594

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/12/2014, 6:04:09 AM · Difficulty 10.6420 · 6,305,146 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ffbfaf7d8cbdd0b313869025d48b982c50581607d66d0784d67d49afc7c6279

Height

#487,594

Difficulty

10.642007

Transactions

5

Size

1.22 KB

Version

2

Bits

0aa45a92

Nonce

159,902

Timestamp

4/12/2014, 6:04:09 AM

Confirmations

6,305,146

Merkle Root

9a9eddc644054d9d81428afa46100c42d3708d82b54e1f76c69ed45dbe745fa4
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.

4.593 × 10⁹⁷(98-digit number)
45932874806062131556…89289018279290516481
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
4.593 × 10⁹⁷(98-digit number)
45932874806062131556…89289018279290516481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.186 × 10⁹⁷(98-digit number)
91865749612124263112…78578036558581032961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.837 × 10⁹⁸(99-digit number)
18373149922424852622…57156073117162065921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.674 × 10⁹⁸(99-digit number)
36746299844849705245…14312146234324131841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.349 × 10⁹⁸(99-digit number)
73492599689699410490…28624292468648263681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.469 × 10⁹⁹(100-digit number)
14698519937939882098…57248584937296527361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.939 × 10⁹⁹(100-digit number)
29397039875879764196…14497169874593054721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.879 × 10⁹⁹(100-digit number)
58794079751759528392…28994339749186109441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.175 × 10¹⁰⁰(101-digit number)
11758815950351905678…57988679498372218881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.351 × 10¹⁰⁰(101-digit number)
23517631900703811356…15977358996744437761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.703 × 10¹⁰⁰(101-digit number)
47035263801407622713…31954717993488875521
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,585,903 XPM·at block #6,792,739 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.