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Block #2,752,700

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2018, 9:06:34 AM Β· Difficulty 11.6503 Β· 4,081,097 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
903545769560964bf162cf08c75709dad254a78b8713e23e9e2aef08861e767b
View on Chainz β†—

Height

#2,752,700

Difficulty

11.650326

Transactions

3

Size

8.45 KB

Version

2

Bits

0ba67bc6

Nonce

539,112,641

Timestamp

7/17/2018, 9:06:34 AM

Confirmations

4,081,097

Mined by

⛏️ P2SHARdutDQ1xSbp1quLmwu8s8wnzpzGjRc33b

Merkle Root

2904d2b095e0ec9ffc16524ddc5d5dd0922c860985484ae897c9de99a09bc303
Transactions (3)
Coinbaseca86feae4da5af…672e06c8013231
1 in β†’ 1 out7.4500 XPM110 B
ARdutDQ1…zGjRc33b
e5b83502cda5e9…fcc8c6d9ce9e9b
5 in β†’ 2 out30000.0101 XPM819 B
AVeBw3y1…1oFFJ3vvAWjPeVFy…S7JHJ1QH
83fe5a06d54190…f17cb2a67b10ef
51 in β†’ 2 out509.9000 XPM7.45 KB
AKTSsnB4…9WbTa5BVARsiPW1r…oR9DimrE
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.

2.234 Γ— 10⁹⁴(95-digit number)
22340520815371666970…35822729067040007361
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
2.234 Γ— 10⁹⁴(95-digit number)
22340520815371666970…35822729067040007361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.468 Γ— 10⁹⁴(95-digit number)
44681041630743333940…71645458134080014721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.936 Γ— 10⁹⁴(95-digit number)
89362083261486667881…43290916268160029441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.787 Γ— 10⁹⁡(96-digit number)
17872416652297333576…86581832536320058881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.574 Γ— 10⁹⁡(96-digit number)
35744833304594667152…73163665072640117761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.148 Γ— 10⁹⁡(96-digit number)
71489666609189334304…46327330145280235521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.429 Γ— 10⁹⁢(97-digit number)
14297933321837866860…92654660290560471041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.859 Γ— 10⁹⁢(97-digit number)
28595866643675733721…85309320581120942081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.719 Γ— 10⁹⁢(97-digit number)
57191733287351467443…70618641162241884161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.143 Γ— 10⁹⁷(98-digit number)
11438346657470293488…41237282324483768321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.287 Γ— 10⁹⁷(98-digit number)
22876693314940586977…82474564648967536641
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:57,914,598 XPMΒ·at block #6,833,796 Β· updates every 60s
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