Block #485,819

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/11/2014, 6:57:27 AM · Difficulty 10.6133 · 6,321,372 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
480144b2534dad9780598ad2c57f1eaa587703c6a8ece66714656cc502c71482

Height

#485,819

Difficulty

10.613312

Transactions

2

Size

413 B

Version

2

Bits

0a9d01fc

Nonce

83,280

Timestamp

4/11/2014, 6:57:27 AM

Confirmations

6,321,372

Merkle Root

8feb4bd0b26a0d6b69c535dd02edde9f9611868b6e9f8a2571028f10005fe4c9
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.

1.864 × 10⁹⁷(98-digit number)
18642778841591191845…11420424719672680801
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
1.864 × 10⁹⁷(98-digit number)
18642778841591191845…11420424719672680801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.728 × 10⁹⁷(98-digit number)
37285557683182383690…22840849439345361601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.457 × 10⁹⁷(98-digit number)
74571115366364767380…45681698878690723201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.491 × 10⁹⁸(99-digit number)
14914223073272953476…91363397757381446401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.982 × 10⁹⁸(99-digit number)
29828446146545906952…82726795514762892801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.965 × 10⁹⁸(99-digit number)
59656892293091813904…65453591029525785601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.193 × 10⁹⁹(100-digit number)
11931378458618362780…30907182059051571201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.386 × 10⁹⁹(100-digit number)
23862756917236725561…61814364118103142401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.772 × 10⁹⁹(100-digit number)
47725513834473451123…23628728236206284801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.545 × 10⁹⁹(100-digit number)
95451027668946902246…47257456472412569601
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:57,701,540 XPM·at block #6,807,190 · updates every 60s
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