Block #2,469,088

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/12/2018, 6:53:43 AM · Difficulty 10.9600 · 4,376,288 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4b8aa82270adca9b8bf165517108ba44e89925cc122c5822c3d638f00fcaf8ef

Height

#2,469,088

Difficulty

10.960028

Transactions

2

Size

427 B

Version

2

Bits

0af5c467

Nonce

1,477,515,616

Timestamp

1/12/2018, 6:53:43 AM

Confirmations

4,376,288

Merkle Root

2c71c0ee2154ab114d8f5996c48d21baebdefcda5094a4b71a9e8fc16e6da951
Transactions (2)
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.

4.020 × 10⁹⁶(97-digit number)
40203102654523410656…87294295405020023041
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
4.020 × 10⁹⁶(97-digit number)
40203102654523410656…87294295405020023041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.040 × 10⁹⁶(97-digit number)
80406205309046821312…74588590810040046081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.608 × 10⁹⁷(98-digit number)
16081241061809364262…49177181620080092161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.216 × 10⁹⁷(98-digit number)
32162482123618728524…98354363240160184321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.432 × 10⁹⁷(98-digit number)
64324964247237457049…96708726480320368641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.286 × 10⁹⁸(99-digit number)
12864992849447491409…93417452960640737281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.572 × 10⁹⁸(99-digit number)
25729985698894982819…86834905921281474561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.145 × 10⁹⁸(99-digit number)
51459971397789965639…73669811842562949121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.029 × 10⁹⁹(100-digit number)
10291994279557993127…47339623685125898241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.058 × 10⁹⁹(100-digit number)
20583988559115986255…94679247370251796481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.116 × 10⁹⁹(100-digit number)
41167977118231972511…89358494740503592961
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:58,007,452 XPM·at block #6,845,375 · updates every 60s
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