Block #487,532

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/12/2014, 5:10:09 AM · Difficulty 10.6419 · 6,316,138 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
362e71185836ae65a7de1b20951736a64259d19f6db3cac1c893bdd7ecfa9b4a

Height

#487,532

Difficulty

10.641922

Transactions

2

Size

1.02 KB

Version

2

Bits

0aa45503

Nonce

357,114

Timestamp

4/12/2014, 5:10:09 AM

Confirmations

6,316,138

Merkle Root

b03bafe14e33b3d1d6d99478478e991b816a76a03be4d268483f32a5df6946de
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.

1.142 × 10¹⁰¹(102-digit number)
11421447153385210165…51955147394524916641
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
1.142 × 10¹⁰¹(102-digit number)
11421447153385210165…51955147394524916641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.284 × 10¹⁰¹(102-digit number)
22842894306770420330…03910294789049833281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.568 × 10¹⁰¹(102-digit number)
45685788613540840660…07820589578099666561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.137 × 10¹⁰¹(102-digit number)
91371577227081681321…15641179156199333121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.827 × 10¹⁰²(103-digit number)
18274315445416336264…31282358312398666241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.654 × 10¹⁰²(103-digit number)
36548630890832672528…62564716624797332481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.309 × 10¹⁰²(103-digit number)
73097261781665345057…25129433249594664961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.461 × 10¹⁰³(104-digit number)
14619452356333069011…50258866499189329921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.923 × 10¹⁰³(104-digit number)
29238904712666138022…00517732998378659841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.847 × 10¹⁰³(104-digit number)
58477809425332276045…01035465996757319681
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:57,673,396 XPM·at block #6,803,669 · 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.