Block #2,852,408

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/23/2018, 8:52:41 PM · Difficulty 11.7208 · 3,978,620 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bb2aa1816835970f5a0074e0cc797acd676297812f5ae580ff2d947f8569415d

Height

#2,852,408

Difficulty

11.720843

Transactions

8

Size

3.01 KB

Version

2

Bits

0bb8892a

Nonce

1,187,332,026

Timestamp

9/23/2018, 8:52:41 PM

Confirmations

3,978,620

Merkle Root

89c7622c07e5c1ceb381ca4a6d8749bad55bb21b8d4f42fcd143b9652ed15693
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.

1.645 × 10⁹⁵(96-digit number)
16457953472204694128…71373266475499532479
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
1.645 × 10⁹⁵(96-digit number)
16457953472204694128…71373266475499532479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.291 × 10⁹⁵(96-digit number)
32915906944409388257…42746532950999064959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.583 × 10⁹⁵(96-digit number)
65831813888818776515…85493065901998129919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.316 × 10⁹⁶(97-digit number)
13166362777763755303…70986131803996259839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.633 × 10⁹⁶(97-digit number)
26332725555527510606…41972263607992519679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.266 × 10⁹⁶(97-digit number)
52665451111055021212…83944527215985039359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.053 × 10⁹⁷(98-digit number)
10533090222211004242…67889054431970078719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.106 × 10⁹⁷(98-digit number)
21066180444422008484…35778108863940157439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.213 × 10⁹⁷(98-digit number)
42132360888844016969…71556217727880314879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.426 × 10⁹⁷(98-digit number)
84264721777688033939…43112435455760629759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.685 × 10⁹⁸(99-digit number)
16852944355537606787…86224870911521259519
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:57,892,358 XPM·at block #6,831,027 · updates every 60s
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