Block #605,187

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/28/2014, 8:28:27 AM · Difficulty 10.9098 · 6,221,876 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
015bd040033209a35cb8694d9b3a22f2cc235dfd844da2c3fb57e7108aa03916

Height

#605,187

Difficulty

10.909804

Transactions

5

Size

27.79 KB

Version

2

Bits

0ae8e8f0

Nonce

93,242,311

Timestamp

6/28/2014, 8:28:27 AM

Confirmations

6,221,876

Merkle Root

a45d3945704a4781da4baac4de916af7dbb664f12d77f6633a707161e7ea4342
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.

5.926 × 10⁹⁸(99-digit number)
59260199388849662465…45579822451465862401
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
5.926 × 10⁹⁸(99-digit number)
59260199388849662465…45579822451465862401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.185 × 10⁹⁹(100-digit number)
11852039877769932493…91159644902931724801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.370 × 10⁹⁹(100-digit number)
23704079755539864986…82319289805863449601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.740 × 10⁹⁹(100-digit number)
47408159511079729972…64638579611726899201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.481 × 10⁹⁹(100-digit number)
94816319022159459945…29277159223453798401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.896 × 10¹⁰⁰(101-digit number)
18963263804431891989…58554318446907596801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.792 × 10¹⁰⁰(101-digit number)
37926527608863783978…17108636893815193601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.585 × 10¹⁰⁰(101-digit number)
75853055217727567956…34217273787630387201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.517 × 10¹⁰¹(102-digit number)
15170611043545513591…68434547575260774401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.034 × 10¹⁰¹(102-digit number)
30341222087091027182…36869095150521548801
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:57,860,688 XPM·at block #6,827,062 · updates every 60s
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