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Home/Chain Registry/Block #458,822

Block #458,822

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/24/2014, 8:57:54 PM Β· Difficulty 10.4206 Β· 6,339,996 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
48b642aef53f111c1fe884deafba32f5026c89e4237d857b8091e8b053992615
View on Chainz β†—

Height

#458,822

Difficulty

10.420603

Transactions

1

Size

289 B

Version

2

Bits

0a6baca9

Nonce

142,055

Timestamp

3/24/2014, 8:57:54 PM

Confirmations

6,339,996

Merkle Root

eb0c68a20b78c9c6c83d0e86efdfbddb39643802794151d72f366a3a7ce29fb2
Transactions (1)
Coinbaseeb0c68a20b78c9…366a3a7ce29fb2
1 in β†’ 4 out9.1900 XPM199 B
AMVf7Jrg…xd5AVR7CALzzzbUz…2Cb4jSDNAa2Amg89…4rjYrsPZAJno7LX2…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.

7.064 Γ— 10⁹³(94-digit number)
70640766603092039796…55300776264740631040
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
7.064 Γ— 10⁹³(94-digit number)
70640766603092039796…55300776264740631039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.412 Γ— 10⁹⁴(95-digit number)
14128153320618407959…10601552529481262079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.825 Γ— 10⁹⁴(95-digit number)
28256306641236815918…21203105058962524159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.651 Γ— 10⁹⁴(95-digit number)
56512613282473631837…42406210117925048319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.130 Γ— 10⁹⁡(96-digit number)
11302522656494726367…84812420235850096639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.260 Γ— 10⁹⁡(96-digit number)
22605045312989452735…69624840471700193279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.521 Γ— 10⁹⁡(96-digit number)
45210090625978905470…39249680943400386559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.042 Γ— 10⁹⁡(96-digit number)
90420181251957810940…78499361886800773119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.808 Γ— 10⁹⁢(97-digit number)
18084036250391562188…56998723773601546239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.616 Γ— 10⁹⁢(97-digit number)
36168072500783124376…13997447547203092479
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 458822

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 48b642aef53f111c1fe884deafba32f5026c89e4237d857b8091e8b053992615

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 #458,822 on Chainz β†—
Circulating Supply:57,634,572 XPMΒ·at block #6,798,817 Β· updates every 60s
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