Block #2,862,550

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 10/1/2018, 10:44:00 AM · Difficulty 11.6751 · 3,977,991 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a347562641956d5988b8cca423e4d30cdbfd8e287c7b5fbc028368cfc6b1a188

Height

#2,862,550

Difficulty

11.675139

Transactions

19

Size

6.15 KB

Version

2

Bits

0bacd5e7

Nonce

188,117,600

Timestamp

10/1/2018, 10:44:00 AM

Confirmations

3,977,991

Merkle Root

86e83cf87a81baee9b8d6aba88418a2f7d62a50fa565b8d11fb3bbb944772309
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.

1.803 × 10⁹⁵(96-digit number)
18038091125445067481…11091303570849860319
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
1.803 × 10⁹⁵(96-digit number)
18038091125445067481…11091303570849860319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.607 × 10⁹⁵(96-digit number)
36076182250890134963…22182607141699720639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.215 × 10⁹⁵(96-digit number)
72152364501780269926…44365214283399441279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.443 × 10⁹⁶(97-digit number)
14430472900356053985…88730428566798882559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.886 × 10⁹⁶(97-digit number)
28860945800712107970…77460857133597765119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.772 × 10⁹⁶(97-digit number)
57721891601424215940…54921714267195530239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.154 × 10⁹⁷(98-digit number)
11544378320284843188…09843428534391060479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.308 × 10⁹⁷(98-digit number)
23088756640569686376…19686857068782120959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.617 × 10⁹⁷(98-digit number)
46177513281139372752…39373714137564241919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.235 × 10⁹⁷(98-digit number)
92355026562278745505…78747428275128483839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.847 × 10⁹⁸(99-digit number)
18471005312455749101…57494856550256967679
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:57,968,660 XPM·at block #6,840,540 · updates every 60s
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