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Home/Chain Registry/Block #2,832,925

Block #2,832,925

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 9:41:10 AM Β· Difficulty 11.7150 Β· 4,009,309 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8236e416db8abb405f2e0bf737324395bdbd0d20053cde60e887f177f49daa94
View on Chainz β†—

Difficulty

11.714974

Transactions

2

Size

1.43 KB

Version

2

Bits

0bb7088d

Nonce

1,335,771,755

Timestamp

9/10/2018, 9:41:10 AM

Confirmations

4,009,309

Merkle Root

cbd143d1fedef19a6ad934334350745aefa4d24ef06b79e45023fff3e3fd55e2
Transactions (2)
Coinbase1ed06be39b70ee…9ba4c7057a46ec
1 in β†’ 1 out7.2900 XPM110 B
AZtxQr2F…7grUWrUz
625ebfddaff688…8f984977865246
8 in β†’ 2 out1.0100 XPM1.23 KB
ATUjs8BB…rFRyF2pEAJQ1hYhT…aTdPyoiq
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.

6.638 Γ— 10⁹⁴(95-digit number)
66383720149158011221…97846054957568144080
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.638 Γ— 10⁹⁴(95-digit number)
66383720149158011221…97846054957568144079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.327 Γ— 10⁹⁡(96-digit number)
13276744029831602244…95692109915136288159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.655 Γ— 10⁹⁡(96-digit number)
26553488059663204488…91384219830272576319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.310 Γ— 10⁹⁡(96-digit number)
53106976119326408977…82768439660545152639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.062 Γ— 10⁹⁢(97-digit number)
10621395223865281795…65536879321090305279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.124 Γ— 10⁹⁢(97-digit number)
21242790447730563590…31073758642180610559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.248 Γ— 10⁹⁢(97-digit number)
42485580895461127181…62147517284361221119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.497 Γ— 10⁹⁢(97-digit number)
84971161790922254363…24295034568722442239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.699 Γ— 10⁹⁷(98-digit number)
16994232358184450872…48590069137444884479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.398 Γ— 10⁹⁷(98-digit number)
33988464716368901745…97180138274889768959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.797 Γ— 10⁹⁷(98-digit number)
67976929432737803490…94360276549779537919
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2832925

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 8236e416db8abb405f2e0bf737324395bdbd0d20053cde60e887f177f49daa94

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 #2,832,925 on Chainz β†—
Circulating Supply:57,982,270 XPMΒ·at block #6,842,233 Β· updates every 60s
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