1. #6,807,9311CC11 primes

    Cunningham 1st · ⛏️ coinsforall.io

Block #1,109,296

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/16/2015, 6:49:25 AM · Difficulty 10.8547 · 5,698,636 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9121c028790aebae9c2badfb9ad5bd8765cbcd728e045ab6ae871b8aaaac3784

Height

#1,109,296

Difficulty

10.854664

Transactions

2

Size

540 B

Version

2

Bits

0adacb46

Nonce

43,837,409

Timestamp

6/16/2015, 6:49:25 AM

Confirmations

5,698,636

Merkle Root

867dc5e25b95c18b7b493de848356f6d575cdd277839faa5f9a548f4f161d8cc
Transactions (2)
1 in → 1 out8.4800 XPM109 B
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.

7.354 × 10⁹⁷(98-digit number)
73546001649062544508…85728776501467189759
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
7.354 × 10⁹⁷(98-digit number)
73546001649062544508…85728776501467189759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.470 × 10⁹⁸(99-digit number)
14709200329812508901…71457553002934379519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.941 × 10⁹⁸(99-digit number)
29418400659625017803…42915106005868759039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.883 × 10⁹⁸(99-digit number)
58836801319250035607…85830212011737518079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.176 × 10⁹⁹(100-digit number)
11767360263850007121…71660424023475036159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.353 × 10⁹⁹(100-digit number)
23534720527700014242…43320848046950072319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.706 × 10⁹⁹(100-digit number)
47069441055400028485…86641696093900144639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.413 × 10⁹⁹(100-digit number)
94138882110800056971…73283392187800289279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.882 × 10¹⁰⁰(101-digit number)
18827776422160011394…46566784375600578559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.765 × 10¹⁰⁰(101-digit number)
37655552844320022788…93133568751201157119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.531 × 10¹⁰⁰(101-digit number)
75311105688640045577…86267137502402314239
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:57,707,493 XPM·at block #6,807,931 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy