Block #2,930,222

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/19/2018, 4:00:57 PM · Difficulty 11.3904 · 3,914,801 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2f8116a3488ce35405407b613a8d6ed15e37b3133f4c983811242091bc6cda04

Height

#2,930,222

Difficulty

11.390354

Transactions

2

Size

572 B

Version

2

Bits

0b63ee42

Nonce

2,686,904

Timestamp

11/19/2018, 4:00:57 PM

Confirmations

3,914,801

Merkle Root

3c934ad30dba29eb44c2937b4ee614628c7f88a6fdee1a3bc6e6f6a3c9ab8e53
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.

7.798 × 10⁹⁴(95-digit number)
77986235873438329938…71463220605334635801
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
7.798 × 10⁹⁴(95-digit number)
77986235873438329938…71463220605334635801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.559 × 10⁹⁵(96-digit number)
15597247174687665987…42926441210669271601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.119 × 10⁹⁵(96-digit number)
31194494349375331975…85852882421338543201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.238 × 10⁹⁵(96-digit number)
62388988698750663950…71705764842677086401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.247 × 10⁹⁶(97-digit number)
12477797739750132790…43411529685354172801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.495 × 10⁹⁶(97-digit number)
24955595479500265580…86823059370708345601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.991 × 10⁹⁶(97-digit number)
49911190959000531160…73646118741416691201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.982 × 10⁹⁶(97-digit number)
99822381918001062321…47292237482833382401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.996 × 10⁹⁷(98-digit number)
19964476383600212464…94584474965666764801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.992 × 10⁹⁷(98-digit number)
39928952767200424928…89168949931333529601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
7.985 × 10⁹⁷(98-digit number)
79857905534400849857…78337899862667059201
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:58,004,608 XPM·at block #6,845,022 · updates every 60s
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