Block #1,144,095

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/8/2015, 1:07:19 AM · Difficulty 10.9280 · 5,659,361 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ea6ef9ccd9e46b248f4351f80afa34ff1adfa066c2dd16a7b062bd30d3808b15

Height

#1,144,095

Difficulty

10.927996

Transactions

5

Size

2.39 KB

Version

2

Bits

0aed911f

Nonce

447,796,263

Timestamp

7/8/2015, 1:07:19 AM

Confirmations

5,659,361

Merkle Root

12b9a1ba3a0ae81c9ca090dfdef704554075c873ea3190922f9b723a6475ceb2
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.

1.347 × 10⁹⁸(99-digit number)
13472008786133998569…96688745944402915841
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
1.347 × 10⁹⁸(99-digit number)
13472008786133998569…96688745944402915841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.694 × 10⁹⁸(99-digit number)
26944017572267997138…93377491888805831681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.388 × 10⁹⁸(99-digit number)
53888035144535994276…86754983777611663361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.077 × 10⁹⁹(100-digit number)
10777607028907198855…73509967555223326721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.155 × 10⁹⁹(100-digit number)
21555214057814397710…47019935110446653441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.311 × 10⁹⁹(100-digit number)
43110428115628795421…94039870220893306881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.622 × 10⁹⁹(100-digit number)
86220856231257590843…88079740441786613761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.724 × 10¹⁰⁰(101-digit number)
17244171246251518168…76159480883573227521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.448 × 10¹⁰⁰(101-digit number)
34488342492503036337…52318961767146455041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.897 × 10¹⁰⁰(101-digit number)
68976684985006072674…04637923534292910081
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:57,671,675 XPM·at block #6,803,455 · updates every 60s
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