Block #3,092,071

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/14/2019, 2:12:10 AM · Difficulty 11.0503 · 3,751,020 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb8a0f5e3ec238902752e4a80caa092d4fd9586ede4691c74b097badcdaeb69f

Height

#3,092,071

Difficulty

11.050347

Transactions

14

Size

5.85 KB

Version

2

Bits

0b0ce386

Nonce

76,705,727

Timestamp

3/14/2019, 2:12:10 AM

Confirmations

3,751,020

Merkle Root

50595e192a00dd787fb4ce83aeef2d0821ba9474979ba18d47553765a1889f70
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.

1.372 × 10⁹⁶(97-digit number)
13724448059970839577…46696886501399858241
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
1.372 × 10⁹⁶(97-digit number)
13724448059970839577…46696886501399858241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.744 × 10⁹⁶(97-digit number)
27448896119941679154…93393773002799716481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.489 × 10⁹⁶(97-digit number)
54897792239883358309…86787546005599432961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.097 × 10⁹⁷(98-digit number)
10979558447976671661…73575092011198865921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.195 × 10⁹⁷(98-digit number)
21959116895953343323…47150184022397731841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.391 × 10⁹⁷(98-digit number)
43918233791906686647…94300368044795463681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.783 × 10⁹⁷(98-digit number)
87836467583813373294…88600736089590927361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.756 × 10⁹⁸(99-digit number)
17567293516762674658…77201472179181854721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.513 × 10⁹⁸(99-digit number)
35134587033525349317…54402944358363709441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.026 × 10⁹⁸(99-digit number)
70269174067050698635…08805888716727418881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.405 × 10⁹⁹(100-digit number)
14053834813410139727…17611777433454837761
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:57,989,090 XPM·at block #6,843,090 · updates every 60s
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