Block #1,182,196

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/4/2015, 4:14:19 AM · Difficulty 10.9144 · 5,657,477 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
43cb98a3d10e5c5b27112e00612f6a5685812f314322c2cacea36a36d7b782f3

Height

#1,182,196

Difficulty

10.914380

Transactions

2

Size

1.72 KB

Version

2

Bits

0aea14ca

Nonce

269,496,437

Timestamp

8/4/2015, 4:14:19 AM

Confirmations

5,657,477

Merkle Root

837435e7261ab94271ae4f2d66cff6ba8724bf41642d5cce0701ad1860a9eeb1
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.

6.646 × 10⁹²(93-digit number)
66465305721402404668…66064401311321651201
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
6.646 × 10⁹²(93-digit number)
66465305721402404668…66064401311321651201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.329 × 10⁹³(94-digit number)
13293061144280480933…32128802622643302401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.658 × 10⁹³(94-digit number)
26586122288560961867…64257605245286604801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.317 × 10⁹³(94-digit number)
53172244577121923734…28515210490573209601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.063 × 10⁹⁴(95-digit number)
10634448915424384746…57030420981146419201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.126 × 10⁹⁴(95-digit number)
21268897830848769493…14060841962292838401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.253 × 10⁹⁴(95-digit number)
42537795661697538987…28121683924585676801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.507 × 10⁹⁴(95-digit number)
85075591323395077975…56243367849171353601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.701 × 10⁹⁵(96-digit number)
17015118264679015595…12486735698342707201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.403 × 10⁹⁵(96-digit number)
34030236529358031190…24973471396685414401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
6.806 × 10⁹⁵(96-digit number)
68060473058716062380…49946942793370828801
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:57,961,673 XPM·at block #6,839,672 · updates every 60s
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