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Block #2,806,765

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/23/2018, 5:31:29 PM Β· Difficulty 11.6709 Β· 4,035,356 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6bb406258e9d49f34dbe81f3783dc3022aa16f70046046979f6b4c7726267e54
View on Chainz β†—

Height

#2,806,765

Difficulty

11.670890

Transactions

1

Size

201 B

Version

2

Bits

0babbf79

Nonce

1,897,261,823

Timestamp

8/23/2018, 5:31:29 PM

Confirmations

4,035,356

Mined by

⛏️ P2SHAHRRk6RjgpUfGFCsiTLSvdVNxhF1iCqrTX

Merkle Root

00fe5527d5b94b04d17871c731adf58320de2d1e8f7723269e40c0358e35e5b9
Transactions (1)
Coinbase00fe5527d5b94b…40c0358e35e5b9
1 in β†’ 1 out7.3300 XPM110 B
AHRRk6Rj…F1iCqrTX
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.389 Γ— 10⁹⁢(97-digit number)
33894081986655626085…63523314462312744961
Discovered Prime Numbers
p_k = 2^k Γ— 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
3.389 Γ— 10⁹⁢(97-digit number)
33894081986655626085…63523314462312744961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.778 Γ— 10⁹⁢(97-digit number)
67788163973311252170…27046628924625489921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.355 Γ— 10⁹⁷(98-digit number)
13557632794662250434…54093257849250979841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.711 Γ— 10⁹⁷(98-digit number)
27115265589324500868…08186515698501959681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.423 Γ— 10⁹⁷(98-digit number)
54230531178649001736…16373031397003919361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.084 Γ— 10⁹⁸(99-digit number)
10846106235729800347…32746062794007838721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.169 Γ— 10⁹⁸(99-digit number)
21692212471459600694…65492125588015677441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.338 Γ— 10⁹⁸(99-digit number)
43384424942919201388…30984251176031354881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.676 Γ— 10⁹⁸(99-digit number)
86768849885838402777…61968502352062709761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.735 Γ— 10⁹⁹(100-digit number)
17353769977167680555…23937004704125419521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.470 Γ— 10⁹⁹(100-digit number)
34707539954335361111…47874009408250839041
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,981,355 XPMΒ·at block #6,842,120 Β· updates every 60s
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