XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,792,328

Block #2,792,328

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/13/2018, 3:41:25 PM Β· Difficulty 11.6751 Β· 4,038,273 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dca834d4fdfecc52a4e3dd0fc078dc7c48d80d8103b8bf96c8f1d25c30efcc8c
View on Chainz β†—

Difficulty

11.675102

Transactions

1

Size

201 B

Version

2

Bits

0bacd37a

Nonce

1,723,174,726

Timestamp

8/13/2018, 3:41:25 PM

Confirmations

4,038,273

Merkle Root

b7109f98335f299745dd9e5c35e77a7db8281bcd3edf3c1547e60dfdb40114f0
Transactions (1)
Coinbaseb7109f98335f29…e60dfdb40114f0
1 in β†’ 1 out7.3200 XPM110 B
AYogo3ub…tE41bzun
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.

3.333 Γ— 10⁹⁷(98-digit number)
33333635211620800548…79632678693576908800
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
3.333 Γ— 10⁹⁷(98-digit number)
33333635211620800548…79632678693576908799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.666 Γ— 10⁹⁷(98-digit number)
66667270423241601096…59265357387153817599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.333 Γ— 10⁹⁸(99-digit number)
13333454084648320219…18530714774307635199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.666 Γ— 10⁹⁸(99-digit number)
26666908169296640438…37061429548615270399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.333 Γ— 10⁹⁸(99-digit number)
53333816338593280877…74122859097230540799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.066 Γ— 10⁹⁹(100-digit number)
10666763267718656175…48245718194461081599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.133 Γ— 10⁹⁹(100-digit number)
21333526535437312350…96491436388922163199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.266 Γ— 10⁹⁹(100-digit number)
42667053070874624701…92982872777844326399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.533 Γ— 10⁹⁹(100-digit number)
85334106141749249403…85965745555688652799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.706 Γ— 10¹⁰⁰(101-digit number)
17066821228349849880…71931491111377305599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.413 Γ— 10¹⁰⁰(101-digit number)
34133642456699699761…43862982222754611199
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 2792328

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 dca834d4fdfecc52a4e3dd0fc078dc7c48d80d8103b8bf96c8f1d25c30efcc8c

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 #2,792,328 on Chainz β†—
Circulating Supply:57,888,930 XPMΒ·at block #6,830,600 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy