Block #2,110,959

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/11/2017, 2:58:28 AM · Difficulty 10.9033 · 4,732,038 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de1d2fa3766278543b313a153c5677bf7ec4f3cdcd071af22c961cd01ecb785a

Height

#2,110,959

Difficulty

10.903304

Transactions

5

Size

1.37 KB

Version

2

Bits

0ae73ef3

Nonce

299,367,492

Timestamp

5/11/2017, 2:58:28 AM

Confirmations

4,732,038

Merkle Root

883a3563ea212df2222525d554be2ad0c81a09647f4681ae67f12b9826a13c13
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.

1.243 × 10⁹⁶(97-digit number)
12430783328018636815…44602498953072693119
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
1.243 × 10⁹⁶(97-digit number)
12430783328018636815…44602498953072693119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.486 × 10⁹⁶(97-digit number)
24861566656037273630…89204997906145386239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.972 × 10⁹⁶(97-digit number)
49723133312074547260…78409995812290772479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.944 × 10⁹⁶(97-digit number)
99446266624149094521…56819991624581544959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.988 × 10⁹⁷(98-digit number)
19889253324829818904…13639983249163089919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.977 × 10⁹⁷(98-digit number)
39778506649659637808…27279966498326179839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.955 × 10⁹⁷(98-digit number)
79557013299319275617…54559932996652359679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.591 × 10⁹⁸(99-digit number)
15911402659863855123…09119865993304719359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.182 × 10⁹⁸(99-digit number)
31822805319727710246…18239731986609438719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.364 × 10⁹⁸(99-digit number)
63645610639455420493…36479463973218877439
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,988,331 XPM·at block #6,842,996 · updates every 60s
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