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Block #435,543

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/9/2014, 12:26:42 AM Β· Difficulty 10.3525 Β· 6,390,873 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7a28b20d0128610d34d42edd3c4475980a5fade21af616f91b90dca16dceb2c1
View on Chainz β†—

Height

#435,543

Difficulty

10.352531

Transactions

1

Size

203 B

Version

2

Bits

0a5a3f81

Nonce

28,974

Timestamp

3/9/2014, 12:26:42 AM

Confirmations

6,390,873

Merkle Root

8968d9d14f47bd0c663495de8eb54f94e989a926769b0c2af06673a142f274ae
Transactions (1)
Coinbase8968d9d14f47bd…6673a142f274ae
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.

8.923 Γ— 10¹⁰¹(102-digit number)
89236049471781067227…30876473648026972200
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
8.923 Γ— 10¹⁰¹(102-digit number)
89236049471781067227…30876473648026972201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.784 Γ— 10¹⁰²(103-digit number)
17847209894356213445…61752947296053944401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.569 Γ— 10¹⁰²(103-digit number)
35694419788712426890…23505894592107888801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.138 Γ— 10¹⁰²(103-digit number)
71388839577424853781…47011789184215777601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.427 Γ— 10¹⁰³(104-digit number)
14277767915484970756…94023578368431555201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.855 Γ— 10¹⁰³(104-digit number)
28555535830969941512…88047156736863110401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.711 Γ— 10¹⁰³(104-digit number)
57111071661939883025…76094313473726220801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.142 Γ— 10¹⁰⁴(105-digit number)
11422214332387976605…52188626947452441601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.284 Γ— 10¹⁰⁴(105-digit number)
22844428664775953210…04377253894904883201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.568 Γ— 10¹⁰⁴(105-digit number)
45688857329551906420…08754507789809766401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.137 Γ— 10¹⁰⁴(105-digit number)
91377714659103812840…17509015579619532801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 435543

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 7a28b20d0128610d34d42edd3c4475980a5fade21af616f91b90dca16dceb2c1

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 #435,543 on Chainz β†—
Circulating Supply:57,855,461 XPMΒ·at block #6,826,415 Β· updates every 60s
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