XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,871,429

Block #2,871,429

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/7/2018, 5:15:36 PM Β· Difficulty 11.6654 Β· 3,970,759 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
99f3a7fa02e767bf96ef8bdecc4c8fcc413ee8f3e1d1a7c7a6b0d4832d224a5b
View on Chainz β†—

Difficulty

11.665430

Transactions

1

Size

201 B

Version

2

Bits

0baa59a3

Nonce

1,301,808,154

Timestamp

10/7/2018, 5:15:36 PM

Confirmations

3,970,759

Merkle Root

aa6225202456250c8c900c20cf336acbc65b5623131089146742966debc66eea
Transactions (1)
Coinbaseaa622520245625…42966debc66eea
1 in β†’ 1 out7.3400 XPM110 B
AdD8shNQ…qixG92VP
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.

1.484 Γ— 10⁹⁢(97-digit number)
14843024481968129424…83500573402923622400
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
1.484 Γ— 10⁹⁢(97-digit number)
14843024481968129424…83500573402923622399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.968 Γ— 10⁹⁢(97-digit number)
29686048963936258849…67001146805847244799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.937 Γ— 10⁹⁢(97-digit number)
59372097927872517699…34002293611694489599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.187 Γ— 10⁹⁷(98-digit number)
11874419585574503539…68004587223388979199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.374 Γ— 10⁹⁷(98-digit number)
23748839171149007079…36009174446777958399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.749 Γ— 10⁹⁷(98-digit number)
47497678342298014159…72018348893555916799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.499 Γ— 10⁹⁷(98-digit number)
94995356684596028319…44036697787111833599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.899 Γ— 10⁹⁸(99-digit number)
18999071336919205663…88073395574223667199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.799 Γ— 10⁹⁸(99-digit number)
37998142673838411327…76146791148447334399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.599 Γ— 10⁹⁸(99-digit number)
75996285347676822655…52293582296894668799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.519 Γ— 10⁹⁹(100-digit number)
15199257069535364531…04587164593789337599
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 2871429

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 99f3a7fa02e767bf96ef8bdecc4c8fcc413ee8f3e1d1a7c7a6b0d4832d224a5b

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 #2,871,429 on Chainz β†—
Circulating Supply:57,981,897 XPMΒ·at block #6,842,187 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