XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,653,899

Block #2,653,899

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/8/2018, 7:41:25 PM Β· Difficulty 11.7304 Β· 4,188,894 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7fd86f2eb11ef7f5c0788473a69a27ca404c1d3f227726cb228c1fbe94fa726c
View on Chainz β†—

Difficulty

11.730411

Transactions

1

Size

200 B

Version

2

Bits

0bbafc3f

Nonce

1,741,701,492

Timestamp

5/8/2018, 7:41:25 PM

Confirmations

4,188,894

Merkle Root

dd4520666eb232794f0f0587ad5671fd2fa1a9f56474527c715bdb87c07d461a
Transactions (1)
Coinbasedd4520666eb232…5bdb87c07d461a
1 in β†’ 1 out7.2600 XPM109 B
AcEnmxTH…ZZWyVyxi
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.

1.843 Γ— 10⁹⁢(97-digit number)
18438364155096226891…16466675831195540600
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
1.843 Γ— 10⁹⁢(97-digit number)
18438364155096226891…16466675831195540599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.687 Γ— 10⁹⁢(97-digit number)
36876728310192453782…32933351662391081199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.375 Γ— 10⁹⁢(97-digit number)
73753456620384907564…65866703324782162399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.475 Γ— 10⁹⁷(98-digit number)
14750691324076981512…31733406649564324799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.950 Γ— 10⁹⁷(98-digit number)
29501382648153963025…63466813299128649599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.900 Γ— 10⁹⁷(98-digit number)
59002765296307926051…26933626598257299199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.180 Γ— 10⁹⁸(99-digit number)
11800553059261585210…53867253196514598399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.360 Γ— 10⁹⁸(99-digit number)
23601106118523170420…07734506393029196799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.720 Γ— 10⁹⁸(99-digit number)
47202212237046340841…15469012786058393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.440 Γ— 10⁹⁸(99-digit number)
94404424474092681682…30938025572116787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.888 Γ— 10⁹⁹(100-digit number)
18880884894818536336…61876051144233574399
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 2653899

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 7fd86f2eb11ef7f5c0788473a69a27ca404c1d3f227726cb228c1fbe94fa726c

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 #2,653,899 on Chainz β†—
Circulating Supply:57,986,683 XPMΒ·at block #6,842,792 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