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Home/Chain Registry/Block #2,918,093

Block #2,918,093

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/11/2018, 3:05:57 AM Β· Difficulty 11.4093 Β· 3,925,257 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b7a4ab0f74ac375af37d405dd7dfe1422daa5a5d405958189ed4da4fc8f1cbe9
View on Chainz β†—

Difficulty

11.409338

Transactions

1

Size

200 B

Version

2

Bits

0b68ca60

Nonce

590,046,644

Timestamp

11/11/2018, 3:05:57 AM

Confirmations

3,925,257

Merkle Root

092254c893cb559aae8c4a5c45a489c4a82d067281750c146560f70b9f2a9e50
Transactions (1)
Coinbase092254c893cb55…60f70b9f2a9e50
1 in β†’ 1 out7.6700 XPM110 B
AbXwmGxD…4XXYP765
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.

4.558 Γ— 10⁹⁴(95-digit number)
45582672100409095946…90167147468606414320
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
4.558 Γ— 10⁹⁴(95-digit number)
45582672100409095946…90167147468606414321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.116 Γ— 10⁹⁴(95-digit number)
91165344200818191893…80334294937212828641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.823 Γ— 10⁹⁡(96-digit number)
18233068840163638378…60668589874425657281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.646 Γ— 10⁹⁡(96-digit number)
36466137680327276757…21337179748851314561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.293 Γ— 10⁹⁡(96-digit number)
72932275360654553514…42674359497702629121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.458 Γ— 10⁹⁢(97-digit number)
14586455072130910702…85348718995405258241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.917 Γ— 10⁹⁢(97-digit number)
29172910144261821405…70697437990810516481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.834 Γ— 10⁹⁢(97-digit number)
58345820288523642811…41394875981621032961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.166 Γ— 10⁹⁷(98-digit number)
11669164057704728562…82789751963242065921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.333 Γ— 10⁹⁷(98-digit number)
23338328115409457124…65579503926484131841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.667 Γ— 10⁹⁷(98-digit number)
46676656230818914249…31159007852968263681
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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
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 2918093

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 b7a4ab0f74ac375af37d405dd7dfe1422daa5a5d405958189ed4da4fc8f1cbe9

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 #2,918,093 on Chainz β†—
Circulating Supply:57,991,162 XPMΒ·at block #6,843,349 Β· updates every 60s
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