Block #1,200,567

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/19/2015, 3:44:50 PM · Difficulty 10.8147 · 5,594,477 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
518eb900c6e65bb012078315c499b8fbbc07988ddf243465c9217e7e66292549

Height

#1,200,567

Difficulty

10.814742

Transactions

4

Size

1.00 KB

Version

2

Bits

0ad092f4

Nonce

254,714,332

Timestamp

8/19/2015, 3:44:50 PM

Confirmations

5,594,477

Merkle Root

58ec048c235d41b241919ece14efeb2b77b724b03093a8c959d0b92fec594bc8
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.

2.648 × 10⁹⁵(96-digit number)
26489450211034277089…97457360693547653121
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
2.648 × 10⁹⁵(96-digit number)
26489450211034277089…97457360693547653121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.297 × 10⁹⁵(96-digit number)
52978900422068554178…94914721387095306241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.059 × 10⁹⁶(97-digit number)
10595780084413710835…89829442774190612481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.119 × 10⁹⁶(97-digit number)
21191560168827421671…79658885548381224961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.238 × 10⁹⁶(97-digit number)
42383120337654843343…59317771096762449921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.476 × 10⁹⁶(97-digit number)
84766240675309686686…18635542193524899841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.695 × 10⁹⁷(98-digit number)
16953248135061937337…37271084387049799681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.390 × 10⁹⁷(98-digit number)
33906496270123874674…74542168774099599361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.781 × 10⁹⁷(98-digit number)
67812992540247749348…49084337548199198721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.356 × 10⁹⁸(99-digit number)
13562598508049549869…98168675096398397441
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:57,604,391 XPM·at block #6,795,043 · updates every 60s
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