Block #2,646,549

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/3/2018, 10:21:11 AM · Difficulty 11.7513 · 4,191,481 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e2ec62d7948737e28159a5bd4b4a708deed1f6ef75d41da1ba3e94d3d3131c1

Height

#2,646,549

Difficulty

11.751261

Transactions

3

Size

1.94 KB

Version

2

Bits

0bc052a5

Nonce

24,211,839

Timestamp

5/3/2018, 10:21:11 AM

Confirmations

4,191,481

Merkle Root

9687ae4ea4b552e9f0bab634bc360c7777f8db786827806e342b26eb9cd4b16a
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.

2.566 × 10⁹⁴(95-digit number)
25660823019689614295…26636615080130182401
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
2.566 × 10⁹⁴(95-digit number)
25660823019689614295…26636615080130182401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.132 × 10⁹⁴(95-digit number)
51321646039379228590…53273230160260364801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.026 × 10⁹⁵(96-digit number)
10264329207875845718…06546460320520729601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.052 × 10⁹⁵(96-digit number)
20528658415751691436…13092920641041459201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.105 × 10⁹⁵(96-digit number)
41057316831503382872…26185841282082918401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.211 × 10⁹⁵(96-digit number)
82114633663006765744…52371682564165836801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.642 × 10⁹⁶(97-digit number)
16422926732601353148…04743365128331673601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.284 × 10⁹⁶(97-digit number)
32845853465202706297…09486730256663347201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.569 × 10⁹⁶(97-digit number)
65691706930405412595…18973460513326694401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.313 × 10⁹⁷(98-digit number)
13138341386081082519…37946921026653388801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.627 × 10⁹⁷(98-digit number)
26276682772162165038…75893842053306777601
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:57,948,594 XPM·at block #6,838,029 · updates every 60s
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