Block #195,969

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/6/2013, 4:35:38 AM · Difficulty 9.8802 · 6,598,814 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
681c63343d6a1042661498a76ed6a615a5d59b6c80779d267658998ae020bfe5

Height

#195,969

Difficulty

9.880198

Transactions

3

Size

3.24 KB

Version

2

Bits

09e154aa

Nonce

428,268

Timestamp

10/6/2013, 4:35:38 AM

Confirmations

6,598,814

Merkle Root

1363cd60f90bb5eee889f7331287d4a4481830c1fc9d1099fc5e0e7cbf4c65f2
Transactions (3)
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.

1.450 × 10⁹⁷(98-digit number)
14502897010963574544…67281269363802790521
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
1.450 × 10⁹⁷(98-digit number)
14502897010963574544…67281269363802790521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.900 × 10⁹⁷(98-digit number)
29005794021927149088…34562538727605581041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.801 × 10⁹⁷(98-digit number)
58011588043854298176…69125077455211162081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.160 × 10⁹⁸(99-digit number)
11602317608770859635…38250154910422324161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.320 × 10⁹⁸(99-digit number)
23204635217541719270…76500309820844648321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.640 × 10⁹⁸(99-digit number)
46409270435083438540…53000619641689296641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.281 × 10⁹⁸(99-digit number)
92818540870166877081…06001239283378593281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.856 × 10⁹⁹(100-digit number)
18563708174033375416…12002478566757186561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.712 × 10⁹⁹(100-digit number)
37127416348066750832…24004957133514373121
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,602,316 XPM·at block #6,794,782 · updates every 60s
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