Block #936,092

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/14/2015, 12:48:45 PM · Difficulty 10.9012 · 5,890,341 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0039685cc50f14fc6ed046b709546083ef8be06ca8fcc598913a55523fa37d07

Height

#936,092

Difficulty

10.901188

Transactions

3

Size

49.28 KB

Version

2

Bits

0ae6b43a

Nonce

95,628,957

Timestamp

2/14/2015, 12:48:45 PM

Confirmations

5,890,341

Merkle Root

f9d3be1cd24d0a5614e7eeaeb1fe4588f35529b493d6082589cd149478cb3e31
Transactions (3)
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.

2.628 × 10⁹⁷(98-digit number)
26283221860839524770…32019095476853299201
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
2.628 × 10⁹⁷(98-digit number)
26283221860839524770…32019095476853299201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.256 × 10⁹⁷(98-digit number)
52566443721679049541…64038190953706598401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.051 × 10⁹⁸(99-digit number)
10513288744335809908…28076381907413196801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.102 × 10⁹⁸(99-digit number)
21026577488671619816…56152763814826393601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.205 × 10⁹⁸(99-digit number)
42053154977343239633…12305527629652787201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.410 × 10⁹⁸(99-digit number)
84106309954686479266…24611055259305574401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.682 × 10⁹⁹(100-digit number)
16821261990937295853…49222110518611148801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.364 × 10⁹⁹(100-digit number)
33642523981874591706…98444221037222297601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.728 × 10⁹⁹(100-digit number)
67285047963749183413…96888442074444595201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.345 × 10¹⁰⁰(101-digit number)
13457009592749836682…93776884148889190401
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:57,855,600 XPM·at block #6,826,432 · updates every 60s
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