Block #2,752,382

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/17/2018, 4:01:17 AM · Difficulty 11.6493 · 4,081,103 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6db3abc858a1493d2c0c2af6d5eb557feb7964c74d6331a12560ca7549cac70f

Height

#2,752,382

Difficulty

11.649276

Transactions

3

Size

1.21 KB

Version

2

Bits

0ba636fb

Nonce

1,784,742,082

Timestamp

7/17/2018, 4:01:17 AM

Confirmations

4,081,103

Merkle Root

e8463a8d990f15416bc5df101f4faafd13aa085c0364d1756db78c00a3cea753
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.

6.008 × 10⁹⁶(97-digit number)
60080916504315636051…86052019193059082241
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
6.008 × 10⁹⁶(97-digit number)
60080916504315636051…86052019193059082241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.201 × 10⁹⁷(98-digit number)
12016183300863127210…72104038386118164481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.403 × 10⁹⁷(98-digit number)
24032366601726254420…44208076772236328961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.806 × 10⁹⁷(98-digit number)
48064733203452508841…88416153544472657921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.612 × 10⁹⁷(98-digit number)
96129466406905017682…76832307088945315841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.922 × 10⁹⁸(99-digit number)
19225893281381003536…53664614177890631681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.845 × 10⁹⁸(99-digit number)
38451786562762007072…07329228355781263361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.690 × 10⁹⁸(99-digit number)
76903573125524014145…14658456711562526721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.538 × 10⁹⁹(100-digit number)
15380714625104802829…29316913423125053441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.076 × 10⁹⁹(100-digit number)
30761429250209605658…58633826846250106881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
6.152 × 10⁹⁹(100-digit number)
61522858500419211316…17267653692500213761
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:57,912,085 XPM·at block #6,833,484 · updates every 60s
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