Block #2,107,378

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/8/2017, 11:19:45 PM · Difficulty 10.8934 · 4,732,643 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f3146f7af01d2953b9d40f86f448f44b093c3a2176fc5d423e2d08bf00406209

Height

#2,107,378

Difficulty

10.893429

Transactions

2

Size

426 B

Version

2

Bits

0ae4b7c7

Nonce

766,622,203

Timestamp

5/8/2017, 11:19:45 PM

Confirmations

4,732,643

Merkle Root

b52d0d670dc88a7da6fb5b4f864ee008f6e8386fcc874a00e06a5e0fa743a21a
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.

1.547 × 10⁹⁷(98-digit number)
15472434513329152678…79751457769772769279
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
1.547 × 10⁹⁷(98-digit number)
15472434513329152678…79751457769772769279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.094 × 10⁹⁷(98-digit number)
30944869026658305357…59502915539545538559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.188 × 10⁹⁷(98-digit number)
61889738053316610715…19005831079091077119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.237 × 10⁹⁸(99-digit number)
12377947610663322143…38011662158182154239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.475 × 10⁹⁸(99-digit number)
24755895221326644286…76023324316364308479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.951 × 10⁹⁸(99-digit number)
49511790442653288572…52046648632728616959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.902 × 10⁹⁸(99-digit number)
99023580885306577144…04093297265457233919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.980 × 10⁹⁹(100-digit number)
19804716177061315428…08186594530914467839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.960 × 10⁹⁹(100-digit number)
39609432354122630857…16373189061828935679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.921 × 10⁹⁹(100-digit number)
79218864708245261715…32746378123657871359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.584 × 10¹⁰⁰(101-digit number)
15843772941649052343…65492756247315742719
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:57,964,479 XPM·at block #6,840,020 · 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.
Privacy Policy·

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