XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #231,090

Block #231,090

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/28/2013, 5:26:11 AM Β· Difficulty 9.9402 Β· 6,563,936 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
48fe9e81afc36a95033fd526ee6bd37453b616ec163e2be3b0a75ba2f66decbc
View on Chainz β†—

Height

#231,090

Difficulty

9.940222

Transactions

1

Size

199 B

Version

2

Bits

09f0b265

Nonce

15,202

Timestamp

10/28/2013, 5:26:11 AM

Confirmations

6,563,936

Merkle Root

2b124a263ea8a393d65f4f635a3451f8f3d6a8327eb35867e91066e3ff1d6f7f
Transactions (1)
Coinbase2b124a263ea8a3…1066e3ff1d6f7f
1 in β†’ 1 out10.1100 XPM109 B
ANhBYN2S…W53F3KTQ
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.

6.446 Γ— 10⁹⁴(95-digit number)
64463394556588757848…83138809681139821100
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
6.446 Γ— 10⁹⁴(95-digit number)
64463394556588757848…83138809681139821099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.289 Γ— 10⁹⁡(96-digit number)
12892678911317751569…66277619362279642199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.578 Γ— 10⁹⁡(96-digit number)
25785357822635503139…32555238724559284399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.157 Γ— 10⁹⁡(96-digit number)
51570715645271006279…65110477449118568799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.031 Γ— 10⁹⁢(97-digit number)
10314143129054201255…30220954898237137599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.062 Γ— 10⁹⁢(97-digit number)
20628286258108402511…60441909796474275199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.125 Γ— 10⁹⁢(97-digit number)
41256572516216805023…20883819592948550399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.251 Γ— 10⁹⁢(97-digit number)
82513145032433610046…41767639185897100799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.650 Γ— 10⁹⁷(98-digit number)
16502629006486722009…83535278371794201599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 231090

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 48fe9e81afc36a95033fd526ee6bd37453b616ec163e2be3b0a75ba2f66decbc

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 #231,090 on Chainz β†—
Circulating Supply:57,604,255 XPMΒ·at block #6,795,025 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK