Block #1,354,908

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/5/2015, 1:06:21 AM · Difficulty 10.8087 · 5,470,516 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
619377430aa07bd2688fadc811ad6b24f4220038bd980e28e5fe54618c491a6b

Height

#1,354,908

Difficulty

10.808730

Transactions

3

Size

1.43 KB

Version

2

Bits

0acf08ed

Nonce

129,981,508

Timestamp

12/5/2015, 1:06:21 AM

Confirmations

5,470,516

Merkle Root

429a734503697b2f7b633237d35326508667ea5ffd1fc9226ca2d6fd5091cbb6
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.

3.917 × 10⁹⁵(96-digit number)
39172063807547297615…03821350766722837761
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
3.917 × 10⁹⁵(96-digit number)
39172063807547297615…03821350766722837761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.834 × 10⁹⁵(96-digit number)
78344127615094595230…07642701533445675521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.566 × 10⁹⁶(97-digit number)
15668825523018919046…15285403066891351041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.133 × 10⁹⁶(97-digit number)
31337651046037838092…30570806133782702081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.267 × 10⁹⁶(97-digit number)
62675302092075676184…61141612267565404161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.253 × 10⁹⁷(98-digit number)
12535060418415135236…22283224535130808321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.507 × 10⁹⁷(98-digit number)
25070120836830270473…44566449070261616641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.014 × 10⁹⁷(98-digit number)
50140241673660540947…89132898140523233281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.002 × 10⁹⁸(99-digit number)
10028048334732108189…78265796281046466561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.005 × 10⁹⁸(99-digit number)
20056096669464216378…56531592562092933121
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,847,493 XPM·at block #6,825,423 · updates every 60s
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