Block #3,232,363

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/19/2019, 7:03:44 PM · Difficulty 11.0004 · 3,607,044 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c81b0d204be99848b8d80cff8bb3bb1af3709d50cc9a5b9cd70043cffa94af9f

Height

#3,232,363

Difficulty

11.000430

Transactions

5

Size

1.96 KB

Version

2

Bits

0b001c34

Nonce

1,615,260,362

Timestamp

6/19/2019, 7:03:44 PM

Confirmations

3,607,044

Merkle Root

771bfc7860fa43c0ad5480245ccc828a5c955a15247f88d75ff2182a9af3eb3d
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.

2.224 × 10⁹⁸(99-digit number)
22240048359478496810…58392075976509358079
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
2.224 × 10⁹⁸(99-digit number)
22240048359478496810…58392075976509358079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.448 × 10⁹⁸(99-digit number)
44480096718956993620…16784151953018716159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.896 × 10⁹⁸(99-digit number)
88960193437913987240…33568303906037432319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.779 × 10⁹⁹(100-digit number)
17792038687582797448…67136607812074864639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.558 × 10⁹⁹(100-digit number)
35584077375165594896…34273215624149729279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.116 × 10⁹⁹(100-digit number)
71168154750331189792…68546431248299458559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.423 × 10¹⁰⁰(101-digit number)
14233630950066237958…37092862496598917119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.846 × 10¹⁰⁰(101-digit number)
28467261900132475917…74185724993197834239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.693 × 10¹⁰⁰(101-digit number)
56934523800264951834…48371449986395668479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.138 × 10¹⁰¹(102-digit number)
11386904760052990366…96742899972791336959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.277 × 10¹⁰¹(102-digit number)
22773809520105980733…93485799945582673919
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,959,543 XPM·at block #6,839,406 · updates every 60s
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