Block #2,923,699

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/15/2018, 7:10:45 AM · Difficulty 11.3612 · 3,909,207 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
33d8627e793d0de4fb09010c60896b2f4c128b074679d9c527e48d5c57727e7e

Height

#2,923,699

Difficulty

11.361209

Transactions

2

Size

1.28 KB

Version

2

Bits

0b5c782b

Nonce

201,663,479

Timestamp

11/15/2018, 7:10:45 AM

Confirmations

3,909,207

Merkle Root

2da031a6e0a92bd5ea54ceb683f300af62b69449727a3d3036963e1d89e36ac4
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.

2.217 × 10⁹⁶(97-digit number)
22178794442614478640…55224492222884044799
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
2.217 × 10⁹⁶(97-digit number)
22178794442614478640…55224492222884044799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.435 × 10⁹⁶(97-digit number)
44357588885228957280…10448984445768089599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.871 × 10⁹⁶(97-digit number)
88715177770457914561…20897968891536179199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.774 × 10⁹⁷(98-digit number)
17743035554091582912…41795937783072358399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.548 × 10⁹⁷(98-digit number)
35486071108183165824…83591875566144716799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.097 × 10⁹⁷(98-digit number)
70972142216366331649…67183751132289433599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.419 × 10⁹⁸(99-digit number)
14194428443273266329…34367502264578867199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.838 × 10⁹⁸(99-digit number)
28388856886546532659…68735004529157734399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.677 × 10⁹⁸(99-digit number)
56777713773093065319…37470009058315468799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.135 × 10⁹⁹(100-digit number)
11355542754618613063…74940018116630937599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.271 × 10⁹⁹(100-digit number)
22711085509237226127…49880036233261875199
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:57,907,420 XPM·at block #6,832,905 · updates every 60s
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