Block #367,592

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/20/2014, 4:47:43 AM · Difficulty 10.4341 · 6,438,720 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8ee19fc93545633d81a6ab49bf96d38ed5333c63099541eae3e00206e9a4b862

Height

#367,592

Difficulty

10.434100

Transactions

2

Size

1.10 KB

Version

2

Bits

0a6f2131

Nonce

222,171

Timestamp

1/20/2014, 4:47:43 AM

Confirmations

6,438,720

Merkle Root

d5312216fcd12cbeb8cc6ea6b2f89b6709eb813bd2dc9d2b710c0bc1e706ccb4
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.

1.177 × 10⁹⁸(99-digit number)
11771034157873043557…68156492934553463721
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
1.177 × 10⁹⁸(99-digit number)
11771034157873043557…68156492934553463721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.354 × 10⁹⁸(99-digit number)
23542068315746087115…36312985869106927441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.708 × 10⁹⁸(99-digit number)
47084136631492174231…72625971738213854881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.416 × 10⁹⁸(99-digit number)
94168273262984348463…45251943476427709761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.883 × 10⁹⁹(100-digit number)
18833654652596869692…90503886952855419521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.766 × 10⁹⁹(100-digit number)
37667309305193739385…81007773905710839041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.533 × 10⁹⁹(100-digit number)
75334618610387478771…62015547811421678081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.506 × 10¹⁰⁰(101-digit number)
15066923722077495754…24031095622843356161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.013 × 10¹⁰⁰(101-digit number)
30133847444154991508…48062191245686712321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.026 × 10¹⁰⁰(101-digit number)
60267694888309983016…96124382491373424641
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:57,694,584 XPM·at block #6,806,311 · updates every 60s
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