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Block #2,802,462

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2018, 5:55:38 PM Β· Difficulty 11.6703 Β· 4,040,563 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4a3b0fc4a77e4921b1c529a040214cf7f9d3c766de68cfd25b7dd3289e9ba88a
View on Chainz β†—

Height

#2,802,462

Difficulty

11.670270

Transactions

1

Size

200 B

Version

2

Bits

0bab96d7

Nonce

1,769,302,018

Timestamp

8/20/2018, 5:55:38 PM

Confirmations

4,040,563

Mined by

⛏️ P2SHAXC67CpCgYpXgz5nRedV297usdKWGWdKX4

Merkle Root

5ed08be1853abfa23b029905430a5538356116c4735f6e45ade1b43de654a6f5
Transactions (1)
Coinbase5ed08be1853abf…e1b43de654a6f5
1 in β†’ 1 out7.3300 XPM110 B
AXC67CpC…KWGWdKX4
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.

5.611 Γ— 10⁹³(94-digit number)
56119120008880640220…35455576346191030941
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
5.611 Γ— 10⁹³(94-digit number)
56119120008880640220…35455576346191030941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.122 Γ— 10⁹⁴(95-digit number)
11223824001776128044…70911152692382061881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.244 Γ— 10⁹⁴(95-digit number)
22447648003552256088…41822305384764123761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.489 Γ— 10⁹⁴(95-digit number)
44895296007104512176…83644610769528247521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.979 Γ— 10⁹⁴(95-digit number)
89790592014209024352…67289221539056495041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.795 Γ— 10⁹⁡(96-digit number)
17958118402841804870…34578443078112990081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.591 Γ— 10⁹⁡(96-digit number)
35916236805683609741…69156886156225980161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.183 Γ— 10⁹⁡(96-digit number)
71832473611367219482…38313772312451960321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.436 Γ— 10⁹⁢(97-digit number)
14366494722273443896…76627544624903920641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.873 Γ— 10⁹⁢(97-digit number)
28732989444546887792…53255089249807841281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.746 Γ— 10⁹⁢(97-digit number)
57465978889093775585…06510178499615682561
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:57,988,554 XPMΒ·at block #6,843,024 Β· updates every 60s
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