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Home/Chain Registry/Block #423,799

Block #423,799

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/28/2014, 4:25:12 PM Β· Difficulty 10.3782 Β· 6,390,161 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5813e4b4eabb2bb63d32d02e07ba7e3e783dbbda8e9cfb8dab08989ba4dc80dc
View on Chainz β†—

Height

#423,799

Difficulty

10.378171

Transactions

1

Size

210 B

Version

2

Bits

0a60cfcd

Nonce

4,392

Timestamp

2/28/2014, 4:25:12 PM

Confirmations

6,390,161

Merkle Root

3e818a3c5b4d4f3df42f3ae304d70b9cd5b75366411e3161d11ae9ecece98515
Transactions (1)
Coinbase3e818a3c5b4d4f…1ae9ecece98515
1 in β†’ 1 out9.2700 XPM116 B
AbwWkWZt…kawDhufa
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.

7.577 Γ— 10¹⁰⁴(105-digit number)
75771302119127134741…94228843623609324000
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
7.577 Γ— 10¹⁰⁴(105-digit number)
75771302119127134741…94228843623609324001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.515 Γ— 10¹⁰⁡(106-digit number)
15154260423825426948…88457687247218648001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.030 Γ— 10¹⁰⁡(106-digit number)
30308520847650853896…76915374494437296001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.061 Γ— 10¹⁰⁡(106-digit number)
60617041695301707792…53830748988874592001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.212 Γ— 10¹⁰⁢(107-digit number)
12123408339060341558…07661497977749184001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.424 Γ— 10¹⁰⁢(107-digit number)
24246816678120683117…15322995955498368001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.849 Γ— 10¹⁰⁢(107-digit number)
48493633356241366234…30645991910996736001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.698 Γ— 10¹⁰⁢(107-digit number)
96987266712482732468…61291983821993472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.939 Γ— 10¹⁰⁷(108-digit number)
19397453342496546493…22583967643986944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.879 Γ— 10¹⁰⁷(108-digit number)
38794906684993092987…45167935287973888001
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 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
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 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 423799

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 5813e4b4eabb2bb63d32d02e07ba7e3e783dbbda8e9cfb8dab08989ba4dc80dc

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 #423,799 on Chainz β†—
Circulating Supply:57,755,757 XPMΒ·at block #6,813,959 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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