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Home/Chain Registry/Block #2,118,694

Block #2,118,694

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/16/2017, 6:50:00 AM Β· Difficulty 10.9092 Β· 4,723,942 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c82310b0c90b5c84140d76377016dc0fe4dcb326c92fc448bd0c33fa9ab2cbbf
View on Chainz β†—

Difficulty

10.909155

Transactions

1

Size

200 B

Version

2

Bits

0ae8be63

Nonce

950,380,598

Timestamp

5/16/2017, 6:50:00 AM

Confirmations

4,723,942

Merkle Root

48f8cbe125db793bcb9ce85f4d4523d0e3d7529a752c65b222aa8be5a66b1d90
Transactions (1)
Coinbase48f8cbe125db79…aa8be5a66b1d90
1 in β†’ 1 out8.3900 XPM110 B
AdZUSfN4…7Eskxkka
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.

2.088 Γ— 10⁹⁴(95-digit number)
20884489540711422517…87185574733231925480
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
2.088 Γ— 10⁹⁴(95-digit number)
20884489540711422517…87185574733231925481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.176 Γ— 10⁹⁴(95-digit number)
41768979081422845034…74371149466463850961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.353 Γ— 10⁹⁴(95-digit number)
83537958162845690069…48742298932927701921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.670 Γ— 10⁹⁡(96-digit number)
16707591632569138013…97484597865855403841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.341 Γ— 10⁹⁡(96-digit number)
33415183265138276027…94969195731710807681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.683 Γ— 10⁹⁡(96-digit number)
66830366530276552055…89938391463421615361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.336 Γ— 10⁹⁢(97-digit number)
13366073306055310411…79876782926843230721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.673 Γ— 10⁹⁢(97-digit number)
26732146612110620822…59753565853686461441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.346 Γ— 10⁹⁢(97-digit number)
53464293224221241644…19507131707372922881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.069 Γ— 10⁹⁷(98-digit number)
10692858644844248328…39014263414745845761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
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, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2118694

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock c82310b0c90b5c84140d76377016dc0fe4dcb326c92fc448bd0c33fa9ab2cbbf

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,118,694 on Chainz β†—
Circulating Supply:57,985,521 XPMΒ·at block #6,842,635 Β· updates every 60s
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