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Block #441,398

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/13/2014, 2:50:09 AM Β· Difficulty 10.3498 Β· 6,383,245 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3f93640656783f315d80d463228cecf0fc2ca72bfeede3e8888b7464f0b2286e
View on Chainz β†—

Height

#441,398

Difficulty

10.349792

Transactions

1

Size

224 B

Version

2

Bits

0a598bf0

Nonce

74,479

Timestamp

3/13/2014, 2:50:09 AM

Confirmations

6,383,245

Merkle Root

c0ba1b2ffd02213c472bf812b70754ade49d6c4b3a6272abba406956f1a0a003
Transactions (1)
Coinbasec0ba1b2ffd0221…406956f1a0a003
1 in β†’ 2 out9.3200 XPM131 B
AMVf7Jrg…xd5AVR7CAJno7LX2…vo4wdWtY
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.

4.198 Γ— 10¹⁰⁰(101-digit number)
41981872100058789888…39824408851924016000
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
4.198 Γ— 10¹⁰⁰(101-digit number)
41981872100058789888…39824408851924015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.396 Γ— 10¹⁰⁰(101-digit number)
83963744200117579776…79648817703848031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.679 Γ— 10¹⁰¹(102-digit number)
16792748840023515955…59297635407696063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.358 Γ— 10¹⁰¹(102-digit number)
33585497680047031910…18595270815392127999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.717 Γ— 10¹⁰¹(102-digit number)
67170995360094063820…37190541630784255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.343 Γ— 10¹⁰²(103-digit number)
13434199072018812764…74381083261568511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.686 Γ— 10¹⁰²(103-digit number)
26868398144037625528…48762166523137023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.373 Γ— 10¹⁰²(103-digit number)
53736796288075251056…97524333046274047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.074 Γ— 10¹⁰³(104-digit number)
10747359257615050211…95048666092548095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.149 Γ— 10¹⁰³(104-digit number)
21494718515230100422…90097332185096191999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 441398

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 3f93640656783f315d80d463228cecf0fc2ca72bfeede3e8888b7464f0b2286e

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 #441,398 on Chainz β†—
Circulating Supply:57,841,208 XPMΒ·at block #6,824,642 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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