Block #595,682

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 6/20/2014, 12:42:15 PM · Difficulty 10.9361 · 6,206,032 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0cdfe8f5bdc8cca9cc61ccf7f40e77389d2f7ceb5f1ad1e460e0e7469794571d

Height

#595,682

Difficulty

10.936113

Transactions

3

Size

955 B

Version

2

Bits

0aefa517

Nonce

625,060,887

Timestamp

6/20/2014, 12:42:15 PM

Confirmations

6,206,032

Merkle Root

11de47134dd437a1192c5456a0d366e72273b9d301be7c7dec7f4384ec912850
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.

2.980 × 10¹⁰⁰(101-digit number)
29802783543794189042…57962492529663278081
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
2.980 × 10¹⁰⁰(101-digit number)
29802783543794189042…57962492529663278081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.960 × 10¹⁰⁰(101-digit number)
59605567087588378084…15924985059326556161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.192 × 10¹⁰¹(102-digit number)
11921113417517675616…31849970118653112321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.384 × 10¹⁰¹(102-digit number)
23842226835035351233…63699940237306224641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.768 × 10¹⁰¹(102-digit number)
47684453670070702467…27399880474612449281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.536 × 10¹⁰¹(102-digit number)
95368907340141404935…54799760949224898561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.907 × 10¹⁰²(103-digit number)
19073781468028280987…09599521898449797121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.814 × 10¹⁰²(103-digit number)
38147562936056561974…19199043796899594241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.629 × 10¹⁰²(103-digit number)
76295125872113123948…38398087593799188481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.525 × 10¹⁰³(104-digit number)
15259025174422624789…76796175187598376961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.051 × 10¹⁰³(104-digit number)
30518050348845249579…53592350375196753921
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,657,804 XPM·at block #6,801,713 · updates every 60s
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