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Home/Chain Registry/Block #3,004,869

Block #3,004,869

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/11/2019, 10:58:26 AM Β· Difficulty 11.2031 Β· 3,837,256 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ca2b4f7bf2c9d750ac7889df34371b6cef83e25ebfbe309f3635aa3f4948612a
View on Chainz β†—

Difficulty

11.203110

Transactions

2

Size

426 B

Version

2

Bits

0b33ff04

Nonce

1,025,450,963

Timestamp

1/11/2019, 10:58:26 AM

Confirmations

3,837,256

Merkle Root

38abbbe7a404725cf445cc6a6d5f3481761fa258a89870f456cf24bfd65c5d46
Transactions (2)
Coinbaseec7782ea63e50d…73081c3be0b99c
1 in β†’ 1 out7.9600 XPM110 B
AbXwmGxD…4XXYP765
bc8b190b69c004…3c12efa79ff29b
1 in β†’ 2 out5.8016 XPM225 B
AVEfhJ1b…G1HPVjLzAbXwmGxD…4XXYP765
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.

1.056 Γ— 10⁹⁷(98-digit number)
10566033456112936411…77178862881939046400
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.056 Γ— 10⁹⁷(98-digit number)
10566033456112936411…77178862881939046401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.113 Γ— 10⁹⁷(98-digit number)
21132066912225872822…54357725763878092801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.226 Γ— 10⁹⁷(98-digit number)
42264133824451745645…08715451527756185601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.452 Γ— 10⁹⁷(98-digit number)
84528267648903491290…17430903055512371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.690 Γ— 10⁹⁸(99-digit number)
16905653529780698258…34861806111024742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.381 Γ— 10⁹⁸(99-digit number)
33811307059561396516…69723612222049484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.762 Γ— 10⁹⁸(99-digit number)
67622614119122793032…39447224444098969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.352 Γ— 10⁹⁹(100-digit number)
13524522823824558606…78894448888197939201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.704 Γ— 10⁹⁹(100-digit number)
27049045647649117212…57788897776395878401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.409 Γ— 10⁹⁹(100-digit number)
54098091295298234425…15577795552791756801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.081 Γ— 10¹⁰⁰(101-digit number)
10819618259059646885…31155591105583513601
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 3004869

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 ca2b4f7bf2c9d750ac7889df34371b6cef83e25ebfbe309f3635aa3f4948612a

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 #3,004,869 on Chainz β†—
Circulating Supply:57,981,388 XPMΒ·at block #6,842,124 Β· updates every 60s
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