Block #566,904

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/29/2014, 8:16:25 AM · Difficulty 10.9651 · 6,245,747 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
23f7abf50e7ee268db60d1adc8e4bb9f1336807d94258f35d5c09294d0e8ad5b

Height

#566,904

Difficulty

10.965136

Transactions

1

Size

527 B

Version

2

Bits

0af71328

Nonce

569,763

Timestamp

5/29/2014, 8:16:25 AM

Confirmations

6,245,747

Merkle Root

aaf68bc3d14f18979d402374a1b2ffb9d11eea0733fa07f1b012d878cdfec886
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.

5.643 × 10⁹⁵(96-digit number)
56436172633743860040…05924907406265472001
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
5.643 × 10⁹⁵(96-digit number)
56436172633743860040…05924907406265472001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.128 × 10⁹⁶(97-digit number)
11287234526748772008…11849814812530944001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.257 × 10⁹⁶(97-digit number)
22574469053497544016…23699629625061888001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.514 × 10⁹⁶(97-digit number)
45148938106995088032…47399259250123776001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.029 × 10⁹⁶(97-digit number)
90297876213990176065…94798518500247552001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.805 × 10⁹⁷(98-digit number)
18059575242798035213…89597037000495104001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.611 × 10⁹⁷(98-digit number)
36119150485596070426…79194074000990208001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.223 × 10⁹⁷(98-digit number)
72238300971192140852…58388148001980416001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.444 × 10⁹⁸(99-digit number)
14447660194238428170…16776296003960832001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.889 × 10⁹⁸(99-digit number)
28895320388476856340…33552592007921664001
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:57,745,237 XPM·at block #6,812,650 · updates every 60s
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