Block #600,962

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/25/2014, 4:05:26 AM · Difficulty 10.9158 · 6,225,848 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8e4c5840155292c5d6ae629a58bf95f312e421ec2e5379399d4ba7f1d2252db8

Height

#600,962

Difficulty

10.915846

Transactions

2

Size

616 B

Version

2

Bits

0aea74e1

Nonce

81,237,826

Timestamp

6/25/2014, 4:05:26 AM

Confirmations

6,225,848

Merkle Root

c5b1d906f92e05e5416fa487f180e3a7e9d419c447868532cf8ef5d1776b6d6b
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.

2.126 × 10⁹⁸(99-digit number)
21261240192828227471…95570739977116019201
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
2.126 × 10⁹⁸(99-digit number)
21261240192828227471…95570739977116019201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.252 × 10⁹⁸(99-digit number)
42522480385656454942…91141479954232038401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.504 × 10⁹⁸(99-digit number)
85044960771312909884…82282959908464076801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.700 × 10⁹⁹(100-digit number)
17008992154262581976…64565919816928153601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.401 × 10⁹⁹(100-digit number)
34017984308525163953…29131839633856307201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.803 × 10⁹⁹(100-digit number)
68035968617050327907…58263679267712614401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.360 × 10¹⁰⁰(101-digit number)
13607193723410065581…16527358535425228801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.721 × 10¹⁰⁰(101-digit number)
27214387446820131162…33054717070850457601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.442 × 10¹⁰⁰(101-digit number)
54428774893640262325…66109434141700915201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.088 × 10¹⁰¹(102-digit number)
10885754978728052465…32218868283401830401
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:57,858,642 XPM·at block #6,826,809 · updates every 60s
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