XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #441,807

Block #441,807

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/13/2014, 9:41:12 AM Β· Difficulty 10.3494 Β· 6,382,821 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fdea715ef9ceb6cd5b92f71e60bc97588ed6c9312b32638e99a498507cd94c4b
View on Chainz β†—

Height

#441,807

Difficulty

10.349386

Transactions

1

Size

199 B

Version

2

Bits

0a59715a

Nonce

106,685,821

Timestamp

3/13/2014, 9:41:12 AM

Confirmations

6,382,821

Merkle Root

0c0f74e21490d1f30e9e38de801d03f390c9eca77f3e196c5eacef304bedeff8
Transactions (1)
Coinbase0c0f74e21490d1…acef304bedeff8
1 in β†’ 1 out9.3200 XPM109 B
ATVPNWJJ…LR7g9g8k
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.

3.719 Γ— 10⁹³(94-digit number)
37191187692770348656…75968918767961548000
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
3.719 Γ— 10⁹³(94-digit number)
37191187692770348656…75968918767961547999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.438 Γ— 10⁹³(94-digit number)
74382375385540697313…51937837535923095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.487 Γ— 10⁹⁴(95-digit number)
14876475077108139462…03875675071846191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.975 Γ— 10⁹⁴(95-digit number)
29752950154216278925…07751350143692383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.950 Γ— 10⁹⁴(95-digit number)
59505900308432557851…15502700287384767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.190 Γ— 10⁹⁡(96-digit number)
11901180061686511570…31005400574769535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.380 Γ— 10⁹⁡(96-digit number)
23802360123373023140…62010801149539071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.760 Γ— 10⁹⁡(96-digit number)
47604720246746046280…24021602299078143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.520 Γ— 10⁹⁡(96-digit number)
95209440493492092561…48043204598156287999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.904 Γ— 10⁹⁢(97-digit number)
19041888098698418512…96086409196312575999
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 441807

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 fdea715ef9ceb6cd5b92f71e60bc97588ed6c9312b32638e99a498507cd94c4b

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 #441,807 on Chainz β†—
Circulating Supply:57,841,086 XPMΒ·at block #6,824,627 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