Block #2,852,436

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/23/2018, 9:22:10 PM · Difficulty 11.7207 · 3,979,230 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
824e38f64e033127c4f70dc921ccacf62b8b22805790152daa8ec92d959fddf6

Height

#2,852,436

Difficulty

11.720721

Transactions

9

Size

2.35 KB

Version

2

Bits

0bb8812c

Nonce

251,947,753

Timestamp

9/23/2018, 9:22:10 PM

Confirmations

3,979,230

Merkle Root

12fd5340c7f33131c325ad2454e74a98e5ab5d9c2bc37d3fc553bdc9e522a031
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.

1.369 × 10⁹⁵(96-digit number)
13696110265145263674…08881104724796270239
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
1.369 × 10⁹⁵(96-digit number)
13696110265145263674…08881104724796270239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.739 × 10⁹⁵(96-digit number)
27392220530290527349…17762209449592540479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.478 × 10⁹⁵(96-digit number)
54784441060581054698…35524418899185080959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.095 × 10⁹⁶(97-digit number)
10956888212116210939…71048837798370161919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.191 × 10⁹⁶(97-digit number)
21913776424232421879…42097675596740323839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.382 × 10⁹⁶(97-digit number)
43827552848464843758…84195351193480647679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.765 × 10⁹⁶(97-digit number)
87655105696929687517…68390702386961295359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.753 × 10⁹⁷(98-digit number)
17531021139385937503…36781404773922590719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.506 × 10⁹⁷(98-digit number)
35062042278771875007…73562809547845181439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.012 × 10⁹⁷(98-digit number)
70124084557543750014…47125619095690362879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.402 × 10⁹⁸(99-digit number)
14024816911508750002…94251238191380725759
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:57,897,432 XPM·at block #6,831,665 · updates every 60s
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