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Home/Chain Registry/Block #2,833,749

Block #2,833,749

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 11:11:08 PM Β· Difficulty 11.7158 Β· 4,000,279 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e3f8de38b6131865437632069b852bf95287ca77ea7f527a8ac0ccb5a156eb44
View on Chainz β†—

Difficulty

11.715817

Transactions

1

Size

200 B

Version

2

Bits

0bb73fc7

Nonce

721,663,781

Timestamp

9/10/2018, 11:11:08 PM

Confirmations

4,000,279

Merkle Root

6e889c4d18bcfb43eb042b68bc86455907b032d98bacf03f1d9db9a3aa8b35df
Transactions (1)
Coinbase6e889c4d18bcfb…9db9a3aa8b35df
1 in β†’ 1 out7.2700 XPM110 B
ALii3nij…kzZtatT4
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.

4.184 Γ— 10⁹⁴(95-digit number)
41846124282218741489…10803656033512892960
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
4.184 Γ— 10⁹⁴(95-digit number)
41846124282218741489…10803656033512892959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.369 Γ— 10⁹⁴(95-digit number)
83692248564437482979…21607312067025785919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.673 Γ— 10⁹⁡(96-digit number)
16738449712887496595…43214624134051571839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.347 Γ— 10⁹⁡(96-digit number)
33476899425774993191…86429248268103143679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.695 Γ— 10⁹⁡(96-digit number)
66953798851549986383…72858496536206287359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁢(97-digit number)
13390759770309997276…45716993072412574719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.678 Γ— 10⁹⁢(97-digit number)
26781519540619994553…91433986144825149439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.356 Γ— 10⁹⁢(97-digit number)
53563039081239989106…82867972289650298879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.071 Γ— 10⁹⁷(98-digit number)
10712607816247997821…65735944579300597759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.142 Γ— 10⁹⁷(98-digit number)
21425215632495995642…31471889158601195519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.285 Γ— 10⁹⁷(98-digit number)
42850431264991991285…62943778317202391039
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 2833749

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 e3f8de38b6131865437632069b852bf95287ca77ea7f527a8ac0ccb5a156eb44

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 #2,833,749 on Chainz β†—
Circulating Supply:57,916,451 XPMΒ·at block #6,834,027 Β· updates every 60s
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