Block #1,412,274

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/14/2016, 12:07:08 AM · Difficulty 10.8043 · 5,424,290 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
480fb609844b7d62f7e43ce92fd4ef1dc22d27ca8d05a5642ad704d3e89b4715

Height

#1,412,274

Difficulty

10.804304

Transactions

2

Size

904 B

Version

2

Bits

0acde6d8

Nonce

1,890,926,627

Timestamp

1/14/2016, 12:07:08 AM

Confirmations

5,424,290

Merkle Root

8147f47db18481c6435dddc07a4b9e243701da032acb56c3fdbd20bec1103406
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.

9.751 × 10⁹⁵(96-digit number)
97514964381278697846…84209674484493615361
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
9.751 × 10⁹⁵(96-digit number)
97514964381278697846…84209674484493615361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.950 × 10⁹⁶(97-digit number)
19502992876255739569…68419348968987230721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.900 × 10⁹⁶(97-digit number)
39005985752511479138…36838697937974461441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.801 × 10⁹⁶(97-digit number)
78011971505022958276…73677395875948922881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.560 × 10⁹⁷(98-digit number)
15602394301004591655…47354791751897845761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.120 × 10⁹⁷(98-digit number)
31204788602009183310…94709583503795691521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.240 × 10⁹⁷(98-digit number)
62409577204018366621…89419167007591383041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.248 × 10⁹⁸(99-digit number)
12481915440803673324…78838334015182766081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.496 × 10⁹⁸(99-digit number)
24963830881607346648…57676668030365532161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.992 × 10⁹⁸(99-digit number)
49927661763214693297…15353336060731064321
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:57,936,779 XPM·at block #6,836,563 · updates every 60s
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