Block #2,702,366

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 6/12/2018, 2:30:20 PM · Difficulty 11.6301 · 4,130,968 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aa5da05b0cc2226de593a22eb797d37b867da1646c1f500bfff3fca28c358148

Height

#2,702,366

Difficulty

11.630088

Transactions

3

Size

1.47 KB

Version

2

Bits

0ba14d6e

Nonce

1,564,852,050

Timestamp

6/12/2018, 2:30:20 PM

Confirmations

4,130,968

Merkle Root

6d8fc74a463b3dd385517ae3564ab24eb6a7764a249845729c5ece70d27f2dd7
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.

3.636 × 10⁹⁶(97-digit number)
36364716676437908437…87321770801932784641
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
3.636 × 10⁹⁶(97-digit number)
36364716676437908437…87321770801932784641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.272 × 10⁹⁶(97-digit number)
72729433352875816874…74643541603865569281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.454 × 10⁹⁷(98-digit number)
14545886670575163374…49287083207731138561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.909 × 10⁹⁷(98-digit number)
29091773341150326749…98574166415462277121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.818 × 10⁹⁷(98-digit number)
58183546682300653499…97148332830924554241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.163 × 10⁹⁸(99-digit number)
11636709336460130699…94296665661849108481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.327 × 10⁹⁸(99-digit number)
23273418672920261399…88593331323698216961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.654 × 10⁹⁸(99-digit number)
46546837345840522799…77186662647396433921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.309 × 10⁹⁸(99-digit number)
93093674691681045599…54373325294792867841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.861 × 10⁹⁹(100-digit number)
18618734938336209119…08746650589585735681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.723 × 10⁹⁹(100-digit number)
37237469876672418239…17493301179171471361
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:57,910,867 XPM·at block #6,833,333 · updates every 60s
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