Block #593,879

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/19/2014, 1:58:25 AM · Difficulty 10.9395 · 6,220,458 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
29450ea3e7a6f5bc6d9b0d346199d71a29e182ae7ba86f437606485195436613

Height

#593,879

Difficulty

10.939502

Transactions

3

Size

658 B

Version

2

Bits

0af08336

Nonce

398,085,375

Timestamp

6/19/2014, 1:58:25 AM

Confirmations

6,220,458

Merkle Root

2133ecd08d11c7fcb58caa70c300f73052e629bb83d12f8f6b305b57a5b5ba7e
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.

5.268 × 10⁹⁷(98-digit number)
52686096105362519990…67800603468626166801
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
5.268 × 10⁹⁷(98-digit number)
52686096105362519990…67800603468626166801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.053 × 10⁹⁸(99-digit number)
10537219221072503998…35601206937252333601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.107 × 10⁹⁸(99-digit number)
21074438442145007996…71202413874504667201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.214 × 10⁹⁸(99-digit number)
42148876884290015992…42404827749009334401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.429 × 10⁹⁸(99-digit number)
84297753768580031984…84809655498018668801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.685 × 10⁹⁹(100-digit number)
16859550753716006396…69619310996037337601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.371 × 10⁹⁹(100-digit number)
33719101507432012793…39238621992074675201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.743 × 10⁹⁹(100-digit number)
67438203014864025587…78477243984149350401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.348 × 10¹⁰⁰(101-digit number)
13487640602972805117…56954487968298700801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.697 × 10¹⁰⁰(101-digit number)
26975281205945610235…13908975936597401601
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:57,758,758 XPM·at block #6,814,336 · updates every 60s
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