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Home/Chain Registry/Block #434,579

Block #434,579

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/8/2014, 8:51:54 AM Β· Difficulty 10.3487 Β· 6,377,129 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
979600afb479e399d201ebcb4120514c076487e8dc64ea35f0e5459d652f405f
View on Chainz β†—

Height

#434,579

Difficulty

10.348652

Transactions

1

Size

202 B

Version

2

Bits

0a59413d

Nonce

378,306

Timestamp

3/8/2014, 8:51:54 AM

Confirmations

6,377,129

Merkle Root

8e8fb692d32f93b16f1de1df9941f9612e6a5101a860d197cb19f5d19a39fd60
Transactions (1)
Coinbase8e8fb692d32f93…19f5d19a39fd60
1 in β†’ 1 out9.3200 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.101 Γ— 10⁹⁹(100-digit number)
31017311315772131137…57421152591994204850
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
3.101 Γ— 10⁹⁹(100-digit number)
31017311315772131137…57421152591994204849
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.203 Γ— 10⁹⁹(100-digit number)
62034622631544262274…14842305183988409699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.240 Γ— 10¹⁰⁰(101-digit number)
12406924526308852454…29684610367976819399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.481 Γ— 10¹⁰⁰(101-digit number)
24813849052617704909…59369220735953638799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.962 Γ— 10¹⁰⁰(101-digit number)
49627698105235409819…18738441471907277599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.925 Γ— 10¹⁰⁰(101-digit number)
99255396210470819639…37476882943814555199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.985 Γ— 10¹⁰¹(102-digit number)
19851079242094163927…74953765887629110399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.970 Γ— 10¹⁰¹(102-digit number)
39702158484188327855…49907531775258220799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.940 Γ— 10¹⁰¹(102-digit number)
79404316968376655711…99815063550516441599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.588 Γ— 10¹⁰²(103-digit number)
15880863393675331142…99630127101032883199
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 434579

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 979600afb479e399d201ebcb4120514c076487e8dc64ea35f0e5459d652f405f

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 #434,579 on Chainz β†—
Circulating Supply:57,737,775 XPMΒ·at block #6,811,707 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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