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Block #431,030

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/5/2014, 9:50:03 PM Β· Difficulty 10.3456 Β· 6,365,317 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fe229463e36b09bd0fa5499aa785fb84eb6e21c3ec18d26a3b8788c57a5f6a85
View on Chainz β†—

Height

#431,030

Difficulty

10.345603

Transactions

1

Size

206 B

Version

2

Bits

0a58796a

Nonce

2,205

Timestamp

3/5/2014, 9:50:03 PM

Confirmations

6,365,317

Merkle Root

f60e6adfd88a8e080e74b819c2d833fe67760ef0b4ebf69e7a7e683b243b5733
Transactions (1)
Coinbasef60e6adfd88a8e…7e683b243b5733
1 in β†’ 1 out9.3300 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.

2.476 Γ— 10⁹⁡(96-digit number)
24767750638399255538…47519295482094208000
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
2.476 Γ— 10⁹⁡(96-digit number)
24767750638399255538…47519295482094207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.953 Γ— 10⁹⁡(96-digit number)
49535501276798511077…95038590964188415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.907 Γ— 10⁹⁡(96-digit number)
99071002553597022155…90077181928376831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.981 Γ— 10⁹⁢(97-digit number)
19814200510719404431…80154363856753663999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.962 Γ— 10⁹⁢(97-digit number)
39628401021438808862…60308727713507327999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.925 Γ— 10⁹⁢(97-digit number)
79256802042877617724…20617455427014655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.585 Γ— 10⁹⁷(98-digit number)
15851360408575523544…41234910854029311999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.170 Γ— 10⁹⁷(98-digit number)
31702720817151047089…82469821708058623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.340 Γ— 10⁹⁷(98-digit number)
63405441634302094179…64939643416117247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.268 Γ— 10⁹⁸(99-digit number)
12681088326860418835…29879286832234495999
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 431030

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 fe229463e36b09bd0fa5499aa785fb84eb6e21c3ec18d26a3b8788c57a5f6a85

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 #431,030 on Chainz β†—
Circulating Supply:57,614,769 XPMΒ·at block #6,796,346 Β· updates every 60s
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