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Home/Chain Registry/Block #2,826,739

Block #2,826,739

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2018, 3:50:31 AM Β· Difficulty 11.7105 Β· 4,009,935 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
825e8a2fae1664b66f99d5d56504fe949c1c9e25b981b098d39a29b6f3f21f04
View on Chainz β†—

Difficulty

11.710479

Transactions

1

Size

200 B

Version

2

Bits

0bb5e1f1

Nonce

1,557,566,190

Timestamp

9/6/2018, 3:50:31 AM

Confirmations

4,009,935

Merkle Root

ec84465e8b0d5fcfd35652788d808e4bceff8fbf6c80d2f739cf90c78578ead8
Transactions (1)
Coinbaseec84465e8b0d5f…cf90c78578ead8
1 in β†’ 1 out7.2800 XPM110 B
AN2TYCG8…F7umVY89
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.

1.898 Γ— 10⁹⁡(96-digit number)
18983859903144957488…76493139115403924840
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
1.898 Γ— 10⁹⁡(96-digit number)
18983859903144957488…76493139115403924841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.796 Γ— 10⁹⁡(96-digit number)
37967719806289914977…52986278230807849681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.593 Γ— 10⁹⁡(96-digit number)
75935439612579829955…05972556461615699361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.518 Γ— 10⁹⁢(97-digit number)
15187087922515965991…11945112923231398721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.037 Γ— 10⁹⁢(97-digit number)
30374175845031931982…23890225846462797441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.074 Γ— 10⁹⁢(97-digit number)
60748351690063863964…47780451692925594881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.214 Γ— 10⁹⁷(98-digit number)
12149670338012772792…95560903385851189761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.429 Γ— 10⁹⁷(98-digit number)
24299340676025545585…91121806771702379521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.859 Γ— 10⁹⁷(98-digit number)
48598681352051091171…82243613543404759041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.719 Γ— 10⁹⁷(98-digit number)
97197362704102182343…64487227086809518081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.943 Γ— 10⁹⁸(99-digit number)
19439472540820436468…28974454173619036161
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 2826739

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 825e8a2fae1664b66f99d5d56504fe949c1c9e25b981b098d39a29b6f3f21f04

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 #2,826,739 on Chainz β†—
Circulating Supply:57,937,671 XPMΒ·at block #6,836,673 Β· updates every 60s
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