Block #2,864,197

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 10/2/2018, 3:04:46 PM · Difficulty 11.6717 · 3,968,571 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b90ee22ca34f163940f3b9f47567b42bf13d6af541a319a0a2b19c1aaf22dacd

Height

#2,864,197

Difficulty

11.671744

Transactions

5

Size

32.98 KB

Version

2

Bits

0babf765

Nonce

1,569,582,950

Timestamp

10/2/2018, 3:04:46 PM

Confirmations

3,968,571

Merkle Root

d18b41e0051aa6f4d630ef6a52001443ae4e92cab637b0e5a56af9578e65fd44
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.

2.044 × 10⁹³(94-digit number)
20442373545366992597…83623859798322118401
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
2.044 × 10⁹³(94-digit number)
20442373545366992597…83623859798322118401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.088 × 10⁹³(94-digit number)
40884747090733985194…67247719596644236801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.176 × 10⁹³(94-digit number)
81769494181467970389…34495439193288473601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.635 × 10⁹⁴(95-digit number)
16353898836293594077…68990878386576947201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.270 × 10⁹⁴(95-digit number)
32707797672587188155…37981756773153894401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.541 × 10⁹⁴(95-digit number)
65415595345174376311…75963513546307788801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.308 × 10⁹⁵(96-digit number)
13083119069034875262…51927027092615577601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.616 × 10⁹⁵(96-digit number)
26166238138069750524…03854054185231155201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.233 × 10⁹⁵(96-digit number)
52332476276139501049…07708108370462310401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.046 × 10⁹⁶(97-digit number)
10466495255227900209…15416216740924620801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.093 × 10⁹⁶(97-digit number)
20932990510455800419…30832433481849241601
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:57,906,308 XPM·at block #6,832,767 · updates every 60s
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